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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.
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“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]
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“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]
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
Quantum Computation and Quantum Information
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1993) · doi:10.1007/978-1-4899-4541-9 · Cited by 21,230
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,450
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Coherence in Spontaneous Radiation Processes
Dicke, R. H. (1954) · Physical Review · doi:10.1103/physrev.93.99 · Cited by 7,445
Mathematical Methods of Statistics.
Geary, R. C., & Cramer, H. L. (1947) · The Economic Journal · doi:10.2307/2226151 · Cited by 6,095
Separability Criterion for Density Matrices
Peres, A. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.1413 · Cited by 5,191
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
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894
Quantum detection and estimation theory
Helstrom, C. W. (1969) · Journal of Statistical Physics · doi:10.1007/bf01007479 · Cited by 3,776 · cited 1×
“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
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
An Introduction to the Bootstrap.
Buckland, S. T., Efron, B., & Tibshirani, R. J. (1994) · Biometrics · doi:10.2307/2532810 · Cited by 3,236
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
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,160
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
Probabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582
Giovannetti, V., Lloyd, S., & Maccone, L. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.010401 · Cited by 2,440
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
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401
Quantum Measurement and Control
Wiseman, H. M., & Milburn, G. J. (2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511813948 · Cited by 2,280
(1996) · Cited by 2,280
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 1,381
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
Quantum Measurement and Control
Kiefer, C. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/24/249002 · Cited by 1,016
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
Entanglement, Nonlinear Dynamics, and the Heisenberg Limit
Pezzé, L., & Smerzi, A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.100401 · Cited by 880
Self-citationInterferometric 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 864
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
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 668
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
Multipartite entanglement and high-precision metrology
Tóth, G. (2012) · Physical Review A · doi:10.1103/physreva.85.022322 · Cited by 560
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
Self-citationEntanglement and Extreme Spin Squeezing
Sørensen, A. S., & Mølmer, K. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4431 · Cited by 495
A quantum Rosetta stone for interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Journal of Modern Optics · doi:10.1080/0950034021000011536 · Cited by 452
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
Taming Multiparticle Entanglement
Jungnitsch, B., Moroder, T., & Gühne, O. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.190502 · Cited by 341
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 327
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 305
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
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
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
Device-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 265
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
Self-citationDetection 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
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 245
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
A Quantum Rosetta Stone for Interferometry
Lee, H., Kok, P., & Dowling, J. P. (2002) · Civil War Book Review · Cited by 239
Constructing N -qubit entanglement monotones from antilinear operators
Osterloh, A., & Siewert, J. (2005) · Physical Review A · doi:10.1103/physreva.72.012337 · Cited by 193
Four-party unlockable bound entangled state
Smolin, J. A. (2001) · Physical Review A · doi:10.1103/physreva.63.032306 · Cited by 177
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 137
Self-citationHyllus, P., Pezzè, L., & Smerzi, A. (2010) · Physical Review Letters · doi:10.1103/physrevlett.105.120501 · Cited by 130
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 126
Multipartite Bound Entangled States that Violate Bell’s Inequality
Dür, W. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.230402 · Cited by 124
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 121
Self-citationExperimental 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
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 107
Spin 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
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
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
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
Wigner-Yanase skew information as tests for quantum entanglement
Chen, Z. (2005) · Physical Review A · doi:10.1103/physreva.71.052302 · Cited by 75
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
Entanglement Detection in the Vicinity of Arbitrary Dicke States
Duan, L. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.180502 · Cited by 58
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 57
Huber, M., Erker, P., Schimpf, H., Gabriel, A., & Hiesmayr, B. C. (2011) · Physical Review A · doi:10.1103/physreva.83.040301 · Cited by 57
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
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
The Fisher information and convexity (Corresp.)
Cohen, M. (1968) · IEEE Transactions on Information Theory · doi:10.1109/tit.1968.1054175 · Cited by 51
Generalized Smolin states and their properties
Augusiak, R., & Horodecki, P. (2006) · Physical Review A · doi:10.1103/physreva.73.012318 · Cited by 51
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
Self-citationSub 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 29
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
Detection 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
Self-citationTóth, G., Gühne, O., Seevinck, M., & Uffink, J. (2005) · Physical Review A · doi:10.1103/physreva.72.014101 · Cited by 22
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
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
Research works printed but not linked: 1
- M. B. Plenio, 2007, Quant. Inf. Comput., 7, 1
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Metadata
- 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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
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