Fisher information and multiparticle entanglement
Open accessAbstract
The Fisher information $F$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $F$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $\overline{F}$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $\overline{F}$ is able to detect certain bound entangled states.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The bound could be valid for non-Markovian dynamics as long as they admit a representation in terms of a CP map.
“As a result, the bound could be valid for non Markovian dynamics as long as they admit a representation in terms of a CP map [38].”
From Quantum Speed Limits in Open System Dynamics (2013) · cites this paper as [38]
The QFI connects to other aspects of quantum physics, such as quantum phase transition and entanglement witness.
“Apart from quantum metrology, the QFI also connects to other aspects of quantum physics, such as quantum phase transition [18][19][20] and entanglement witness [21,22].”
From Quantum Fisher information matrix and multiparameter estimation (2020) · cites this paper as [21]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601 · see citing works
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500 · see citing works
<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1993) · doi:10.1007/978-1-4899-4541-9 · Cited by 21,230 · see citing works
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118 · see citing works
Coherence in Spontaneous Radiation Processes
Dicke, R. H. (1954) · Physical Review · doi:10.1103/physrev.93.99 · Cited by 7,445 · see citing works
Mathematical Methods of Statistics.
Geary, R. C., & Cramer, H. L. (1947) · The Economic Journal · doi:10.2307/2226151 · Cited by 6,095 · see citing works
Separability Criterion for Density Matrices
Peres, A. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.1413 · Cited by 5,191 · see citing works
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894 · see citing works
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776 · cited 1× · see citing works
“If the estimator is unbiased, that is, its mean value coincides with the true value of the phase shift, 〈θest〉 = θ , then its minimal standard deviation is limited by the bounds [37,38]”
BackgroundEntanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
Separability of mixed states: necessary and sufficient conditions
Horodecki, M., Horodecki, P., & Horodecki, R. (1996) · Physics Letters A · doi:10.1016/s0375-9601(96)00706-2 · Cited by 3,649 · see citing works
An Introduction to the Bootstrap.
Buckland, S. T., Efron, B., & Tibshirani, R. J. (1994) · Biometrics · doi:10.2307/2532810 · Cited by 3,236 · see citing works
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176 · see citing works
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,014 · see citing works
Quantum Detection and Estimation Theory
(1976) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6017-5 · Cited by 2,712 · see citing works
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582 · see citing works
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440 · see citing works
Bell’s theorem without inequalities
Greenberger, D. M., Horne, M. A., Shimony, A., & Zeilinger, A. (1990) · American Journal of Physics · doi:10.1119/1.16243 · Cited by 2,404 · see citing works
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
(1996) · Cited by 2,280 · see citing works
Quantum Measurement and Control
Wiseman, H. M., & Milburn, G. J. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511813948 · Cited by 2,203 · see citing works
SU(2) and SU(1,1) interferometers
Yurke, B., McCall, S. L., & Klauder, J. R. (1986) · Physical Review A · doi:10.1103/physreva.33.4033 · Cited by 1,367 · see citing works
Mixed-state entanglement and distillation: Is there a ‘bound’ entanglement in nature?
Horodecki, M., Horodecki, P., & Horodecki, R. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.5239 · Cited by 1,208 · see citing works
Many-particle entanglement with Bose–Einstein condensates
Sørensen, A. S., Duan, L.-M., Cirac, J. I., & Zoller, P. (2001) · Nature · doi:10.1038/35051038 · Cited by 956 · see citing works
Entanglement, Nonlinear Dynamics, and the Heisenberg Limit
Pezzé, L., & Smerzi, A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.100401 · Cited by 880 · see citing works
Self-citationQuantum Measurement and Control
Kiefer, C. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/24/249002 · Cited by 878 · see citing works
Interferometric detection of optical phase shifts at the Heisenberg limit
Holland, M., & Burnett, K. R. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1355 · Cited by 871 · see citing works
INFORMATION CONTENTS OF DISTRIBUTIONS
Wigner, E. P., & Yanase, M. M. (1963) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.49.6.910 · Cited by 686 · see citing works
Distinguishing three-body from two-body nonseparability by a Bell-type inequality
Svetlichny, G. (1987) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.35.3066 · Cited by 670 · see citing works
Classification of Mixed Three-Qubit States
Acín, A., Bruß, D., Lewenstein, M., & Sanpera, A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.040401 · Cited by 579 · see citing works
Multipartite entanglement and high-precision metrology
Tóth, G. (2012) · Physical Review A · doi:10.1103/physreva.85.022322 · Cited by 560 · see citing works
Experimental Detection of Multipartite Entanglement using Witness Operators
Bourennane, M., Eibl, M., Kurtsiefer, C., Gaertner, S., Weinfurter, H., Gühne, O., Hyllus, P., Bruß, D., Lewenstein, M., & Sanpera, A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.087902 · Cited by 522 · see citing works
Self-citationA quantum Rosetta stone for interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Journal of Modern Optics · doi:10.1080/0950034021000011536 · Cited by 499 · see citing works
Entanglement and Extreme Spin Squeezing
Sørensen, A. S., & Mølmer, K. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4431 · Cited by 495 · see citing works
Induced measures in the space of mixed quantum states
Życzkowski, K., & Sommers, H.-J. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/35/335 · Cited by 427 · see citing works
Taming Multiparticle Entanglement
Jungnitsch, B., Moroder, T., & Gühne, O. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.190502 · Cited by 329 · see citing works
Separability criteria for genuine multiparticle entanglement
Gühne, O., & Seevinck, M. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/5/053002 · Cited by 316 · see citing works
Bell-Type Inequalities to Detect True n -Body Nonseparability
Collins, D., Gisin, N., Popescu, S., Roberts, D., & Scarani, V. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.170405 · Cited by 298 · see citing works
Classification of multiqubit mixed states: Separability and distillability properties
Dür, W., & Cirac, J. I. (2000) · Physical Review A · doi:10.1103/physreva.61.042314 · Cited by 291 · see citing works
Separability and Distillability of Multiparticle Quantum Systems
Dür, W., Cirac, J. I., & Tarrach, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3562 · Cited by 279 · see citing works
Bell inequality, Bell states and maximally entangled states for n qubits
Gisin, N., & Bechmann-Pasquinucci, H. (1998) · Physics Letters A · doi:10.1016/s0375-9601(98)00516-7 · Cited by 270 · see citing works
Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
Kiesel, N., Schmid, C., Tóth, G., Solano, E., & Weinfurter, H. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.063604 · Cited by 262 · see citing works
Self-citationDevice-Independent Witnesses of Genuine Multipartite Entanglement
Bancal, J.-D., Gisin, N., Liang, Y.-C., & Pironio, S. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.250404 · Cited by 260 · see citing works
Detection of High-Dimensional Genuine Multipartite Entanglement of Mixed States
Huber, M., Mintert, F., Gabriel, A., & Hiesmayr, B. C. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.210501 · Cited by 258 · see citing works
Induced measures in the space of mixed quantum states
Zyczkowski, K., & Sommers, H.-J. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 245 · see citing works
Multipartite entanglement in spin chains
Gühne, O., Tóth, G., & Briegel, H. J. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/229 · Cited by 239 · see citing works
A Quantum Rosetta Stone for Interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Civil War Book Review · Cited by 239 · see citing works
Constructing N -qubit entanglement monotones from antilinear operators
Osterloh, A., & Siewert, J. (2005) · Physical Review A · doi:10.1103/physreva.72.012337 · Cited by 195 · see citing works
Four-party unlockable bound entangled state
Smolin, J. A. (2001) · Physical Review A · doi:10.1103/physreva.63.032306 · Cited by 177 · see citing works
Not all pure entangled states are useful for sub-shot-noise interferometry
Hyllus, P., Gühne, O., & Smerzi, A. (2010) · Physical Review A · doi:10.1103/physreva.82.012337 · Cited by 130 · see citing works
Self-citationHyllus, P., Pezzè, L., & Smerzi, A. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.120501 · Cited by 126 · see citing works
Self-citationSufficient conditions for three-particle entanglement and their tests in recent experiments
Seevinck, M., & Uffink, J. (2001) · Physical Review A · doi:10.1103/physreva.65.012107 · Cited by 125 · see citing works
Multipartite Bound Entangled States that Violate Bell’s Inequality
Dür, W. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.230402 · Cited by 120 · see citing works
Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation
Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Hyllus, P., Pezzè, L., & Smerzi, A. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.080504 · Cited by 120 · see citing works
Self-citationMultipartite entanglement detection from correlation tensors
de Vicente, J. I., & Huber, M. (2011) · Physical Review A · doi:10.1103/physreva.84.062306 · Cited by 110 · see citing works
Experimental Observation of an Entire Family of Four-Photon Entangled States
Wieczorek, W., Schmid, C., Kiesel, N., Pohlner, R., Gühne, O., & Weinfurter, H. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.010503 · Cited by 108 · see citing works
Self-citationSpin Squeezing Inequalities for Arbitrary Spin
Vitagliano, G., Hyllus, P., Egusquiza, I. L., & Tóth, G. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.240502 · Cited by 101 · see citing works
Self-citationQuantifying Multipartite Nonlocality
Bancal, J.-D., Branciard, C., Gisin, N., & Pironio, S. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.090503 · Cited by 98 · see citing works
Quantifying quantumness and the quest for Queens of Quantum
Giraud, O., Braun, P. A., & Braun, D. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/6/063005 · Cited by 94 · see citing works
Multipartite Entanglement Detection via Structure Factors
Krammer, P., Kampermann, H., Bruß, D., Bertlmann, R. A., Kwek, L. C., & Macchiavello, C. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.100502 · Cited by 77 · see citing works
Wigner-Yanase skew information as tests for quantum entanglement
Chen, Z. (2005) · Physical Review A · doi:10.1103/physreva.71.052302 · Cited by 73 · see citing works
Optimal state for keeping reference frames aligned and the platonic solids
Kolenderski, P. L., & Demkowicz-Dobrzański, R. (2008) · Physical Review A · doi:10.1103/physreva.78.052333 · Cited by 64 · see citing works
Entanglement Detection in the Vicinity of Arbitrary Dicke States
Duan, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.180502 · Cited by 58 · see citing works
Huber, M., Erker, P., Schimpf, H., Gabriel, A., & Hiesmayr, B. C. (2011) · Physical Review A · doi:10.1103/physreva.83.040301 · Cited by 56 · see citing works
Configuration of Separability and Tests for Multipartite Entanglement in Bell-Type Experiments
Nagata, K., Koashi, M., & Imoto, N. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.260401 · Cited by 56 · see citing works
Classifying N -Qubit Entanglement via Bell’s Inequalities
Yu, S., Chen, Z., Pan, J.-W., & Zhang, Y.-D. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.080401 · Cited by 53 · see citing works
Energy and multipartite entanglement in multidimensional and frustrated spin models
Gühne, O., & Tóth, G. (2006) · Physical Review A · doi:10.1103/physreva.73.052319 · Cited by 53 · see citing works
The Fisher information and convexity (Corresp.)
Cohen, M. (1968) · IEEE Transactions on Information Theory · doi:10.1109/tit.1968.1054175 · Cited by 51 · see citing works
Generalized Smolin states and their properties
Augusiak, R., & Horodecki, P. (2006) · Physical Review A · doi:10.1103/physreva.73.012318 · Cited by 50 · see citing works
Discriminating Multipartite Entangled States
Schmid, C., Kiesel, N., Laskowski, W., Wieczorek, W., Żukowski, M., & Weinfurter, H. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.200407 · Cited by 37 · see citing works
Self-citationVerifying Genuine High-Order Entanglement
Li, C., Chen, K., Reingruber, A., Chen, Y.-N., & Pan, J.-W. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.210504 · Cited by 28 · see citing works
Sub shot-noise interferometric phase sensitivity with beryllium ions Schrödinger cat states
Pezzè, L., & Smerzi, A. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/78/30004 · Cited by 28 · see citing works
Self-citationDetection of N -particle entanglement with generalized Bell inequalities
Laskowski, W., & Żukowski, M. (2005) · Physical Review A · doi:10.1103/physreva.72.062112 · Cited by 24 · see citing works
Self-citationTóth, G., Gühne, O., Seevinck, M., & Uffink, J. (2005) · Physical Review A · doi:10.1103/physreva.72.014101 · Cited by 22 · see citing works
Multipartite Entanglement Inequalities via Spin Vector Geometry
Durkin, G. A., & Simon, C. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.180402 · Cited by 17 · see citing works
A witness of multipartite entanglement strata
Kaszlikowski, D., & Kay, A. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/5/053026 · Cited by 14 · see citing works
Flagged first, then by citations
1 of the 80 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Colloquium : Quantum coherence as a resource
Streltsov, A., Adesso, G., & Plenio, M. B. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.041003 · Cited by 1,787 · see citing works
Quantum metrology with nonclassical states of atomic ensembles
Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R., & Treutlein, P. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035005 · Cited by 1,705 · see citing works
“The inequalities (48) have been generalized to arbitrary spin systems (Vitagliano et al., 2014, 2011) and to systems of fluctuating numbers of particles (Hyllus et al., 2012b).”
BackgroundSelf-citationQuantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/42/424006 · Cited by 862 · see citing works
Quantum Fisher information matrix and multiparameter estimation
Liu, J., Yuan, H., Lu, X.-M., & Wang, X. (2020) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/ab5d4d · Cited by 802 · see citing works
Quantum metrology from a quantum information science perspective
Tóth, G., & Apellaniz, I. (2014) · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · Cited by 672 · see citing works
Multipartite entanglement and high-precision metrology
Tóth, G. (2012) · Physical Review A · doi:10.1103/physreva.85.022322 · Cited by 560 · see citing works
Quantum Limits in Optical Interferometry
Demkowicz-Dobrzański, R., Jarzyna, M., & Kołodyński, J. (2015) · Progress in optics · doi:10.1016/bs.po.2015.02.003 · Cited by 521 · see citing works
“Above results imply that QFI, or precision, can be interpreted as a particle-entanglement witness, i.e. all states that give precision scaling better than the shot noise must be particleentangled (Hyllus et al., 2012; Tóth, 2012).”
BackgroundQuantum Speed Limits in Open System Dynamics
del Campo, A., Egusquiza, I. L., Plenio, M. B., & Huelga, S. F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.050403 · Cited by 493 · see citing works
Quantum-enhanced measurements without entanglement
Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M. W., & Pirandola, S. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035006 · Cited by 434 · see citing works
“If ρ is k-producible, i.e., it is a convex mixture of pure states which are tensor products of at most k-qubit states, then the quantum Fisher information is bounded above as follows (Hyllus et al., 2012; Tóth, 2012), Iθ(ρ, Jl) ≤ nk2 + (N − nk)2 , (18) where n is the integer part of N/k.”
BackgroundPolino, E., Valeri, M., Spagnolo, N., & Sciarrino, F. (2020) · AVS Quantum Science · doi:10.1116/5.0007577 · Cited by 413 · see citing works
Entanglement certification from theory to experiment
Friis, N., Vitagliano, G., Malik, M., & Huber, M. (2018) · Nature Reviews Physics · doi:10.1038/s42254-018-0003-5 · Cited by 378 · see citing works
“Entanglement depth criteria similar to the above have also been derived for different target states, like Dicke states [108, 285] and planar quantum squeezed states [109, 286], and also based on other quantities, like the QFI [179, 287–290].”
BackgroundMeasuring multipartite entanglement through dynamic susceptibilities
Hauke, P., Heyl, M., Tagliacozzo, L., & Zoller, P. (2016) · Nature Physics · doi:10.1038/nphys3700 · Cited by 362 · see citing works
“The multipartite entanglement that the QFI detects has an immediate interpretation as a resource for quantum metrology [8, 9].”
BackgroundMethodInfluentialQuantum optics of chiral spin networks
Pichler, H., Ramos, T., Daley, A. J., & Zoller, P. (2015) · Physical Review A · doi:10.1103/physreva.91.042116 · Cited by 347 · see citing works
Dissipative phase transition in a central spin system
Kessler, E. M., Giedke, G., İmamoğlu, A., Yelin, S. F., Lukin, M. D., & Cirac, J. I. (2012) · Physical Review A · doi:10.1103/physreva.86.012116 · Cited by 342 · see citing works
Fisher information under decoherence in Bloch representation
Zhong, W., Sun, Z., Ma, J., Wang, X., & Nori, F. (2013) · Physical Review A · doi:10.1103/physreva.87.022337 · Cited by 320 · see citing works
Simulating quantum many-body dynamics on a current digital quantum computer
Smith, A., Kim, M. S., Pollmann, F., & Knolle, J. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0217-0 · Cited by 304 · see citing works
“The QFI is an entanglement witness [65–67], and for our chosen defi-nition in Eq.”
BackgroundGeometric perspective on quantum parameter estimation
Sidhu, J. S., & Kok, P. (2020) · AVS Quantum Science · doi:10.1116/1.5119961 · Cited by 253 · see citing works
Detecting Multiparticle Entanglement of Dicke States
Lücke, B., Peise, J., Vitagliano, G., Arlt, J., Santos, L., Tóth, G., & Klempt, C. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.155304 · Cited by 245 · see citing works
Bounds on the capacity and power of quantum batteries
Julià-Farré, S., Salamon, T., Riera, A., Bera, M. N., & Lewenstein, M. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023113 · Cited by 239 · see citing works
Macroscopic quantum states: Measures, fragility, and implementations
Fröwis, F., Sekatski, P., Dür, W., Gisin, N., & Sangouard, N. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.025004 · Cited by 227 · see citing works
“An effective size of Neff & k implies genuine entanglement within groups of at least k spins (this statement can be made fully rigorous including O(1) correction terms (Hyllus et al., 2012; Tóth, 2012)).”
BackgroundLewis-Swan, R. J., Safavi-Naini, A., Bollinger, J. J., & Rey, A. M. (2019) · Nature Communications · doi:10.1038/s41467-019-09436-y · Cited by 205 · see citing works
“The QFI quantifies the maximal precision with which a parameter δφ in the unitary of Ŵ can be estimated using an interferometric protocol with an input quantum state |Ψ(t)〉, while simultaneously serving as a witness to multipartite entanglement (5; 42; 43; 44).”
MethodQuantum Spin Dimers from Chiral Dissipation in Cold-Atom Chains
Ramos, T., Pichler, H., Daley, A. J., & Zoller, P. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.237203 · Cited by 204 · see citing works
Optimal measurements for simultaneous quantum estimation of multiple phases
Pezzè, L., Ciampini, M. A., Spagnolo, N., Humphreys, P. C., Datta, A., Walmsley, I. A., Barbieri, M., Sciarrino, F., & Smerzi, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.130504 · Cited by 200 · see citing works
Self-citationQuantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks
Schmitt, M., & Heyl, M. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.100503 · Cited by 221 · see citing works
Scrambling and entanglement spreading in long-range spin chains
Pappalardi, S., Russomanno, A., Žunkovič, B., Iemini, F., Silva, A., & Fazio, R. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.134303 · Cited by 193 · see citing works
Thermometry in the quantum regime: recent theoretical progress
Mehboudi, M., Sanpera, A., & Correa, L. A. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab2828 · Cited by 188 · see citing works
Quantum thermal machines and batteries
Bhattacharjee, S., & Dutta, A. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00235-3 · Cited by 185 · see citing works
Genuine quantum correlations in quantum many-body systems: a review of recent progress
Chiara, G. D., & Sanpera, A. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aabf61 · Cited by 174 · see citing works
Sensitivity bounds for multiparameter quantum metrology
Gessner, M., Pezzè, L., & Smerzi, A. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.130503 · Cited by 169 · see citing works
Self-citationNonclassicality as a Quantifiable Resource for Quantum Metrology
Kwon, H., Tan, K. C., Volkoff, T. J., & Jeong, H. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.040503 · Cited by 165 · see citing works
Gebhart, V., Santagati, R., Gentile, A. A., Gauger, E. M., Craig, D., Ares, N., Banchi, L., Marquardt, F., Pezzè, L., & Bonato, C. (2023) · Nature Reviews Physics · doi:10.1038/s42254-022-00552-1 · Cited by 169 · see citing works
Self-citationMultipartite Entanglement Witnesses
Sperling, J., & Vogel, W. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.110503 · Cited by 163 · see citing works
Extremal properties of the variance and the quantum Fisher information
Tóth, G., & Petz, D. (2013) · Physical Review A · doi:10.1103/physreva.87.032324 · Cited by 157 · see citing works
Loschmidt echo for quantum metrology
Macrì, T., Smerzi, A., & Pezzè, L. (2016) · Physical Review A · doi:10.1103/physreva.94.010102 · Cited by 156 · see citing works
Self-citationCriticality-Enhanced Quantum Sensing via Continuous Measurement
Ilias, T., Yang, D., Huelga, S. F., & Plenio, M. B. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010354 · Cited by 156 · see citing works
Entanglement and Spin Squeezing in Non-Hermitian Phase Transitions
Lee, T. E., Reiter, F., & Moiseyev, N. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.250401 · Cited by 150 · see citing works
Observation of Stark many-body localization without disorder
Morong, W., Liu, F., Becker, P., Collins, K. S., Feng, L., Kyprianidis, A., Pagano, G., You, T., Gorshkov, A. V., & Monroe, C. R. (2021) · Nature · doi:10.1038/s41586-021-03988-0 · Cited by 154 · see citing works
Frérot, I., & Roscilde, T. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.020402 · Cited by 149 · see citing works
Detecting Large Quantum Fisher Information with Finite Measurement Precision
Fröwis, F., Sekatski, P., & Dür, W. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.090801 · Cited by 147 · see citing works
Relating Out-of-Time-Order Correlations to Entanglement via Multiple-Quantum Coherences
Gärttner, M., Hauke, P., & Rey, A. M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.040402 · Cited by 145 · see citing works
Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors
Kaubruegger, R., Silvi, P., Kokail, C., van Bijnen, R., Rey, A. M., Ye, J., Kaufman, A. M., & Zoller, P. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.260505 · Cited by 133 · see citing works
At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
Rams, M. M., Sierant, P., Dutta, O., Horodecki, P., & Zakrzewski, J. (2018) · Physical Review X · doi:10.1103/physrevx.8.021022 · Cited by 160 · see citing works
“The rotation scenario serves also as a powerful entanglement detector [23,24] that can detect a vanishing fraction of entanglement [25] or even bound entanglement [26] with scaling close to the Heisenberg limit.”
BackgroundMeasures of macroscopicity for quantum spin systems
Fröwis, F., & Dür, W. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/093039 · Cited by 126 · see citing works
Multipartite Entanglement in Topological Quantum Phases
Pezzè, L., Gabbrielli, M., Lepori, L., & Smerzi, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.250401 · Cited by 117 · see citing works
Self-citationGeneral framework for quantum macroscopicity in terms of coherence
Yadin, B., & Vedral, V. (2016) · Physical Review A · doi:10.1103/physreva.93.022122 · Cited by 114 · see citing works
Synchronization of interacting quantum dipoles
Zhu, B., Schachenmayer, J., Xu, M., Herrera, F., Restrepo, J. G., Holland, M. J., & Rey, A. M. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/8/083063 · Cited by 107 · see citing works
Evaluating Convex Roof Entanglement Measures
Tóth, G., Moroder, T., & Gühne, O. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.160501 · Cited by 106 · see citing works
Quantum-enhanced multiparameter estimation in multiarm interferometers
Ciampini, M. A., Spagnolo, N., Vitelli, C., Pezzè, L., Smerzi, A., & Sciarrino, F. (2016) · Scientific Reports · doi:10.1038/srep28881 · Cited by 104 · see citing works
“The right-hand side inequality in Eqs (4) and (5) is saturated if and only if the FIM is diagonal.”
BackgroundBridging entanglement dynamics and chaos in semiclassical systems
Lerose, A., & Pappalardi, S. (2020) · Physical Review A · doi:10.1103/physreva.102.032404 · Cited by 105 · see citing works
Entanglement-enhanced quantum metrology: From standard quantum limit to Heisenberg limit
Huang, J., Zhuang, M., & Lee, C. (2024) · Applied Physics Reviews · doi:10.1063/5.0204102 · Cited by 105 · see citing works
Random Bosonic States for Robust Quantum Metrology
Oszmaniec, M., Augusiak, R., Gogolin, C., Kołodyński, J., Acín, A., & Lewenstein, M. (2016) · Physical Review X · doi:10.1103/physrevx.6.041044 · Cited by 99 · see citing works
“Quantum-enhanced parameter sensitivity can only be observed with systems exhibiting interparticle entanglement [19]; thus, such enhanced sensitivity can be used to detect multipartite entanglement [20–23] and lower bound the number of particles being entangled [24,25].”
BackgroundMetrological Nonlinear Squeezing Parameter
Gessner, M., Smerzi, A., & Pezzè, L. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.090503 · Cited by 93 · see citing works
“[75] In fact a sharper bound for N-qubit states with up to k entangled qubits [74] is given as ξ−2 opt[ρ̂, Ĥ, Ĥ] ≤ sk2 + r2 where s = bN/kc and r = N − sk.”
Self-citationQuantum Fisher Information from Randomized Measurements
Rath, A., Branciard, C., Minguzzi, A., & Vermersch, B. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.260501 · Cited by 91 · see citing works
Entanglement between Identical Particles Is a Useful and Consistent Resource
Morris, B., Yadin, B., Fadel, M., Zibold, T., Treutlein, P., & Adesso, G. (2020) · Physical Review X · doi:10.1103/physrevx.10.041012 · Cited by 89 · see citing works
“Then, for any particle-separable state, we have F (ρ, n · S) ≤ 1 [52, 53].”
BackgroundKind of entanglement that speeds up quantum evolution
Fröwis, F. (2012) · Physical Review A · doi:10.1103/physreva.85.052127 · Cited by 87 · see citing works
Witnessing entanglement in quantum magnets using neutron scattering
Scheie, A. O., Laurell, P., Samarakoon, A., Lake, B., Nagler, S. E., Granroth, G. E., Okamoto, S., Alvarez, G., & Tennant, D. M. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.224434 · Cited by 85 · see citing works
“[41] Philipp Hyllus, Wiesław Laskowski, Roland Krischek, Christian Schwemmer, Witlef Wieczorek, Harald Weinfurter, Luca Pezzé, and Augusto Smerzi, “Fisher information and multiparticle entanglement,” Phys.”
InfluentialGraph States as a Resource for Quantum Metrology
Shettell, N., & Markham, D. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.110502 · Cited by 85 · see citing works
Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth
Liang, Y.-C., Rosset, D., Bancal, J.-D., Pütz, G., Barnea, T. J., & Gisin, N. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.190401 · Cited by 80 · see citing works
Origin of the slow growth of entanglement entropy in long-range interacting spin systems
Lerose, A., & Pappalardi, S. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.012041 · Cited by 86 · see citing works
Metrological Detection of Multipartite Entanglement from Young Diagrams
Ren, Z., Li, W., Smerzi, A., & Gessner, M. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.080502 · Cited by 80 · see citing works
“In this context, metrological entanglement criteria are powerful tools that establish a quantitative link between the number of detected entangled parties and the quantum gain in interferometric measurements [8–12].”
BackgroundMethodInfluentialSelf-citationSpin squeezing and entanglement for an arbitrary spin
Vitagliano, G., Apellaniz, I., Egusquiza, I. L., & Tóth, G. (2014) · Physical Review A · doi:10.1103/physreva.89.032307 · Cited by 73 · see citing works
Experimental Comparison of Efficient Tomography Schemes for a Six-Qubit State
Schwemmer, C., Tóth, G., Niggebaum, A., Moroder, T., Gross, D., Gühne, O., & Weinfurter, H. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.040503 · Cited by 78 · see citing works
Self-citationQuantifying and Controlling Entanglement in the Quantum Magnet Cs2CoCl4
Laurell, P., Scheie, A. O., Mukherjee, C. J., Koza, M. M., Enderle, M., Tylczyński, Z., Okamoto, S., Coldea, R., Tennant, D. M., & Alvarez, G. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.037201 · Cited by 77 · see citing works
Enhancement of parameter-estimation precision in noisy systems by dynamical decoupling pulses
Tan, Q.-S., Huang, Y., Yin, X., Kuang, L.-M., & Wang, X. (2013) · Physical Review A · doi:10.1103/physreva.87.032102 · Cited by 76 · see citing works
Critical behavior of dissipative two-dimensional spin lattices
Rota, R., Storme, F., Bartolo, N., Fazio, R., & Ciuti, C. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.134431 · Cited by 74 · see citing works
Witnessing entanglement without entanglement witness operators
Pezzè, L., Li, Y., Li, W., & Smerzi, A. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1603346113 · Cited by 70 · see citing works
“In this case, the above method can be extended as a witness of multiparticle entanglement (22, 23): The inequality”
MethodSelf-citationEfficient entanglement criteria for discrete, continuous, and hybrid variables
Gessner, M., Pezzè, L., & Smerzi, A. (2016) · Physical Review A · doi:10.1103/physreva.94.020101 · Cited by 75 · see citing works
“[48] to the case of unequal, arbitrary subsystems.”
BackgroundSelf-citationQuantum States with a Positive Partial Transpose are Useful for Metrology
Tóth, G., & Vértesi, T. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.020506 · Cited by 72 · see citing works
“There have been results concerning entanglement criteria with several quantum Fisher information terms detecting PPT entangled states as well as concerning the metrological usefulness of multipartite states that are not PPT with respect to all bipartions [6,13,14].”
BackgroundClock–Work Trade-Off Relation for Coherence in Quantum Thermodynamics
Kwon, H., Jeong, H., Jennings, D., Yadin, B., & Kim, M. S. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.150602 · Cited by 68 · see citing works
Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed
Gessner, M., & Smerzi, A. (2018) · Physical Review A · doi:10.1103/physreva.97.022109 · Cited by 71 · see citing works
Self-citationCharacterization of Topological States via Dual Multipartite Entanglement
Zhang, Y.-R., Zeng, Y., Fan, H., You, J. Q., & Nori, F. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.250501 · Cited by 69 · see citing works
Phase damping destroys quantum Fisher information of W states
Özaydin, F. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.08.035 · Cited by 67 · see citing works
Heyl, M. (2017) · Physical Review B · doi:10.1103/physrevb.95.060504 · Cited by 69 · see citing works
Frequentist and Bayesian Quantum Phase Estimation
Li, Y., Pezzè, L., Gessner, M., Ren, Z., Li, W., & Smerzi, A. (2018) · Entropy · doi:10.3390/e20090628 · Cited by 64 · see citing works
Self-citationImproving cold-atom sensors with quantum entanglement: Prospects and challenges
Szigeti, S. S., Hosten, O., & Haine, S. A. (2021) · Applied Physics Letters · doi:10.1063/5.0050235 · Cited by 70 · see citing works
Multipartite Entanglement at Finite Temperature
Gabbrielli, M., Smerzi, A., & Pezzè, L. (2018) · Scientific Reports · doi:10.1038/s41598-018-31761-3 · Cited by 65 · see citing works
Self-citationMathew, G., da Silva, S. L. L., Jain, A., Mohan, A., Adroja, D. T., Sakai, V. G., Tomy, C. V., Banerjee, A., Rajendar, G., N., A. V., et al. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043329 · Cited by 61 · see citing works
Geometric perspective on quantum parameter estimation
Sidhu, J. S., & Kok, P. (2020) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 58 · see citing works
Quantum dynamics of disordered spin chains with power-law interactions
Safavi-Naini, A., Wall, M. L., Acevedo, O. L., Rey, A. M., & Nandkishore, R. (2019) · Physical Review A · doi:10.1103/physreva.99.033610 · Cited by 59 · see citing works
Many-Body Nonlocality as a Resource for Quantum-Enhanced Metrology
Niezgoda, A., & Chwedeńczuk, J. (2021) · Physical Review Letters · doi:10.1103/physrevlett.126.210506 · Cited by 58 · see citing works
Phase-sensitivity bounds for two-mode interferometers
Pezzè, L., Hyllus, P., & Smerzi, A. (2015) · Physical Review A · doi:10.1103/physreva.91.032103 · Cited by 56 · see citing works
Self-citationEfficiently solving the dynamics of many-body localized systems at strong disorder
Tomasi, G. D., Pollmann, F., & Heyl, M. (2018) · Physical review B · doi:10.1103/physrevb.99.241114 · Cited by 33 · see citing works
Experimental estimation of the quantum Fisher information from randomized measurements
Yu, M., Li, D., Wang, J., Chu, Y., Yang, P., Gong, M., Goldman, N., & Cai, J. (2021) · Physical Review Research · doi:10.1103/physrevresearch.3.043122 · Cited by 58 · see citing works
“[18] Philipp Hyllus, Wiesław Laskowski, Roland Krischek, Christian Schwemmer, Witlef Wieczorek, Harald Weinfurter, Luca Pezzé, and Augusto Smerzi, “Fisher information and multiparticle entanglement,” Phys.”
BackgroundSingle-copy entanglement detection
Dimić, A., & Dakić, B. (2018) · npj Quantum Information · doi:10.1038/s41534-017-0055-x · Cited by 55 · see citing works
Genuine multipartite entanglement of quantum states in the multiple-copy scenario
Palazuelos, C., & de Vicente, J. I. (2022) · Quantum · doi:10.22331/q-2022-06-13-735 · Cited by 33 · see citing works
Quantum Metrology: Surpassing the shot-noise limit with Dzyaloshinskii-Moriya interaction
Özaydin, F., & Altıntaṣ, A. A. (2015) · Scientific Reports · doi:10.1038/srep16360 · Cited by 54 · see citing works
Reconstructing the quantum critical fan of strongly correlated systems using quantum correlations
Frérot, I., & Roscilde, T. (2019) · Nature Communications · doi:10.1038/s41467-019-08324-9 · Cited by 54 · see citing works
Extensive Multipartite Entanglement from su(2) Quantum Many-Body Scars
Desaules, J.-Y., Pietracaprina, F., Papić, Z., Goold, J., & Pappalardi, S. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.020601 · Cited by 56 · see citing works
Multipartite entanglement in the measurement-induced phase transition of the quantum Ising chain
Paviglianiti, A., & Silva, A. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.184302 · Cited by 54 · see citing works
“[45] and [46], this quantity can be used to witness multipartite entanglement when Ô = Ô[{nj}] = 12 ∑ j nj · σ̂j , where nj are unit vectors.”
BackgroundEntanglement and extreme spin squeezing for a fluctuating number of indistinguishable particles
Hyllus, P., Pezzè, L., Smerzi, A., & Tóth, G. (2012) · Physical Review A · doi:10.1103/physreva.86.012337 · Cited by 50 · see citing works
Self-citationQuantum-limited Euler angle measurements using anticoherent states
Goldberg, A. Z., & James, D. F. V. (2018) · Physical Review A · doi:10.1103/physreva.98.032113 · Cited by 52 · see citing works
Quantum variance: A measure of quantum coherence and quantum correlations for many-body systems
Frérot, I., & Roscilde, T. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.075121 · Cited by 50 · see citing works
Entanglement criterion for multipartite systems based on quantum Fisher information
Akbari-Kourbolagh, Y., & Azhdargalam, M. (2019) · Physical Review A · doi:10.1103/physreva.99.012304 · Cited by 48 · see citing works
Multipartite Entanglement Structure in the Eigenstate Thermalization Hypothesis.
Brenes, M., Pappalardi, S., Goold, J., & Silva, A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.124.040605 · Cited by 35 · see citing works
Probing quantum correlations in many-body systems: a review of scalable methods
Frérot, I., Fadel, M., & Lewenstein, M. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acf8d7 · Cited by 52 · see citing works
Algebraic many-body localization and its implications on information propagation
Tomasi, G. D. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.054204 · Cited by 50 · see citing works
Sciara, S., Reimer, C., Kues, M., Roztocki, P., Cino, A. C., Moss, D., Caspani, L., Munro, W. J., & Morandotti, R. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.120501 · Cited by 49 · see citing works
Haine, S. A. (2018) · Physical Review A · doi:10.1103/physreva.98.030303 · Cited by 48 · see citing works
Machine-Designed Sensor to Make Optimal Use of Entanglement-Generating Dynamics for Quantum Sensing
Haine, S. A., & Hope, J. J. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.060402 · Cited by 48 · see citing works
“Assuming an initial state with no interparticle entanglement (ie, a coherent spin state (CSS) [28]), the maximum possible value is f0 = N , or FQ = NT 2 [17, 18], which we define as the shot-noise limit.”
BackgroundDetection of genuine tripartite entanglement by multiple sequential observers
Maity, A. G., Das, D., Ghosal, A., Roy, A., & Majumdar, A. S. (2020) · Physical Review A · doi:10.1103/physreva.101.042340 · Cited by 47 · see citing works
“[4] P.”
Background
- Authors
- Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., & Smerzi, A.
- Affiliations
- University of the Basque Country (ES)
- University of Gdańsk (PL)
- Max Planck Institute of Quantum Optics (DE)
- University of Trento (IT)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-02-16
- Volume
- 85
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2041209858
- Cited by
- 593
- References
- 80
- Citations by year
- 2026: 44 · 2025: 80 · 2024: 74 · 2023: 52 · 2022: 38 · 2021: 57 · 2020: 43 · 2019: 46 · 2018: 32 · 2017: 33 · 2016: 32 · 2015: 31 · 2014: 16 · 2013: 9 · 2012: 6
- FWCI
- 19.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- INO Open Portal (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- Fisher information, multipartite entanglement, quantum phase estimation, quantum interferometry, shot-noise limit, entanglement detection, bound entangled states, quantum metrology
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
