The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Simultaneous weak measurement of non-commuting observables: a generalized Arthurs-Kelly protocol
Abstract
In contrast to a projective quantum measurement, in a weak measurement the system is only weakly perturbed while only partial information on the measured observable is obtained. A simultaneous measurement of non-commuting observables cannot be projective, however the strongest possible such measurement can be defined as providing their values at the smallest uncertainty limit. Starting with the Arthurs and Kelly (AK) protocol for such measurement of position and momentum, we derive a systematic extension to a corresponding weak measurement along three steps: First, a plausible form of the weak measurement operator analogous to the Gaussian Kraus operator, often used to model a weak measurement of a single observable, is obtained by projecting a naïve extension (valid for commuting observable) onto the corresponding Gabor space. Second, we show that the so obtained set of measurement operators satisfies the normalization condition for the probability to obtain given values of the position and momentum in the weak measurement operation, namely that this set constitutes a positive operator valued measure (POVM) in the position-momentum space. Finally, we show that the so-obtained measurement operator corresponds to a generalization of the AK measurement protocol in which the initial detector wavefunctions is suitable broadened.
Overview
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
Verification
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 check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“In postselected weak measurement technique, the weak value of nonlocal joint operators can not be obtained exactly and the efficieny is too low for entangled state case [32].”
From Direct measurement methods of density matrix of an entangled quantum state (2020) · cites this paper as [32]
Experimental — accuracy not yet measuredIn the citing paper
“If we assume that the polarizers represented by the projection operator π ij and π DD causing displacement along x and y directions, respectively, we can get the weak average of π DD π ij by using the method introduced in Refs.[11,32] as”
From Direct measurement methods of density matrix of an entangled quantum state (2020) · cites this paper as [32]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
States, Effects, and Operations Fundamental Notions of Quantum Theory
(1983) · Lecture Notes in Physics · doi:10.1007/3-540-12732-1 · Cited by 1,565
Research works printed but not linked: 23
- Arthurs, E. & Kelly, J. L. On the simultaneous measurement of a pair of conjugate observables. Bell Syst. Tech. J. 44, 725 (1965). · DOI
- She, C. Y. & Heffner, H. Simultaneous Measurement of Noncommuting Observables. Phys. Rev. 152, 1103 (1966). · DOI
- Braunstein, S. L., Caves, C. M. & Milburn, G. J. Interpretation for a positive P representation. Phys. Rev. A 43, 1153 (1991). · DOI
- Kurotani, Y., Sagawa, T. & Ueda, M. Upper bound on our knowledge about noncommuting observables for a qubit system. Phys. Rev. A 76, 022325 (2007). · DOI
- Allahverdyan, A. E., Balian, R. & Nieuwenhuizen, T. M. Simultaneous measurement of non-commuting observables. Physica E: Low Dimens. Syst. Nanostruct. 42, 339 (2010). · DOI
- Ruskov, R., Korotkov, A. N. & Mølmer, K. Qubit State Monitoring by Measurement of Three Complementary Observables. Phys. Rev. Lett. 105, 100506 (2010). · DOI
- Allahverdyan, A. E., Balian, R. & Nieuwenhuizen, T. M. Understanding quantum measurement from the solution of dynamical models. Phys. Rep. 525, 1 (2013). · DOI
- Bullock, T. J. & Busch, P. Focusing in Arthurs-Kelly-Type Joint Measurements with Correlated Probes. Phys. Rev. Lett. 113, 120401 (2014). · DOI
- García-Pintos, L. P. & Dressel, J. Probing quantumness with joint continuous measurements of noncommuting qubit observables. Phys. Rev. A 94, 062119 (2016). · DOI
- Heinosaari, T. Simultaneous measurement of two quantum observables: Compatibility, broadcasting, and in-between. Phys. Rev. A 93, 042118 (2016). · DOI
- Perarnau-Llobet, M. & Nieuwenhuizen, T. M. Simultaneous measurement of two noncommuting quantum variables: Solution of a dynamical model. Phys. Rev. A 95, 052129 (2017). · DOI
- Chantasri, A. et al. Simultaneous continuous measurement of non-commuting observables: quantum state correlations. arXiv:1706.09670 (2017). · DOI
- Hacohen-Gourgy, S. et al. Quantum dynamics of simultaneously measured non-commuting observables. Nature 538, 491 (2016). · DOI
- Piacentini, F. et al. Measuring Incompatible Observables by Exploiting Sequential Weak Values. Phys. Rev. Lett. 117, 170402 (2016). · DOI
- Neumann, J. V. Mathematical Foundations of Quantum Mechanics (Princeton Univ. Press, Princeton, N.J., 1955).
- Bednorz, A., Belzig, W. & Nitzan, A. Nonclassical time correlation functions in continuous quantum measurement. New J. Phys. 14 (2012). · DOI
- Jacobs, K. & Steck, D. A. A straightforward introduction to continuous quantum measurement. Contemp. Phys. 47, 279 (2006). · DOI
- Korotkov, A. N. Selective quantum evolution of a qubit state due to continuous measurement. Phys. Rev. B 63, 115403 (2001). · DOI
- Atalaya, J., Hacohen-Gourgy, S., Martin, L. S., Siddiqi, I. & Korotkov, A. N. Correlators in simultaneous measurement of non-commuting qubit observables. arXiv:1702.08077 (2017). · DOI
- Jordan, A. N., Chantasri, A., Rouchon, P. & Huard, B. Anatomy of fluorescence: quantum trajectory statistics from continuously measuring spontaneous emission. Quantum Stud.: Math. Found. 3, 237 (2016). · DOI
- Wiseman, H. M. & Milburn, G. J. Quantum theory of optical feedback via homodyne detection. Phys. Rev. Lett. 70, 548 (1993). · DOI
- Yuen, H. & Shapiro, J. Optical communication with two-photon coherent states–Part III: Quantum measurements realizable with photoemissive detectors. IEEE Trans. Inf. Theory 26.1, 78–92 (1980). · DOI
- Ockeloen-Korppi, C. F. et al. Noiseless quantum measurement and squeezing of microwave fields utilizing mechanical vibrations. Phys. Rev. Lett. 118, 103601 (2017). · DOI
Cited by
Sorted by citations
Direct measurement methods of density matrix of an entangled quantum state
Turek, Y. (2020) · Journal of Physics Communications · doi:10.1088/2399-6528/ab9938 · Cited by 4
Metadata
- Authors
- Ochoa, M. A., Belzig, W., & Nitzan, A.
- Venue
- Scientific Reports
- Published
- 2018-10-25
- Volume
- 8
- Issue
- 1
- ISSN
- 2045-2322
- PMC
- PMC6202392
- Cited by
- 20
- References
- 1
- Language
- en
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
