Peres-Horodecki Separability Criterion for Continuous Variable Systems
Open accessAbstract
The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable states. For all bipartite Gaussian states, the Peres-Horodecki criterion turns out to be a necessary and sufficient condition for separability.
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?
In steady state, none of the approaches generate entanglement; the two-mode Gaussian state is separable according to the separability criterion for continuous variable systems.
“It should be noted that in steady state none of the approaches generate entanglement.The two-mode Gaussian state is a separable state according to the separability criterion for continuous variable systems [22,23].”
From The local approach to quantum transport may violate the second law of thermodynamics (2014) · cites this paper as [22]
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
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283 · 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
Unconditional Quantum Teleportation
Furusawa, A., Sørensen, J. L., Braunstein, S. L., Fuchs, C. A., Kimble, H. J., & Polzik, E. S. (1998) · Science · doi:10.1126/science.282.5389.706 · Cited by 3,005 · see citing works
Inseparability Criterion for Continuous Variable Systems
Duan, L.-M., Giedke, G., Cirac, J. I., & Zoller, P. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2722 · Cited by 2,064 · see citing works
Teleportation of Continuous Quantum Variables
Braunstein, S. L., & Kimble, H. J. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.869 · Cited by 1,761 · see citing works
DiVincenzo, D. P. (1995) · Science · doi:10.1126/science.270.5234.255 · Cited by 1,651 · see citing works
Separability criterion and inseparable mixed states with positive partial transposition
Horodecki, P. (1997) · Physics Letters A · doi:10.1016/s0375-9601(97)00416-7 · Cited by 1,297 · see citing works
Quantum Computation Over Continuous Variables
Lloyd, S., & Braunstein, S. L. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1784 · Cited by 1,145 · see citing works
Teleportation of quantum states
Lev Vaidman, A. (1994) · Physical Review A · doi:10.1103/physreva.49.1473 · Cited by 891 · see citing works
The semiclassical evolution of wave packets
Littlejohn, R. G. (1986) · Physics Reports · doi:10.1016/0370-1573(86)90103-1 · Cited by 599 · see citing works
Quantum Information and Computation
Bennett, C. H. (1995) · Physics Today · doi:10.1063/1.881452 · Cited by 574 · see citing works
Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms
Simon, R., Mukunda, N., & Dutta, B. (1994) · Physical Review A · doi:10.1103/physreva.49.1567 · Cited by 466 · see citing works
Self-citationGaussian-Wigner distributions in quantum mechanics and optics
Simon, R., Sudarshan, E. C. G., & Mukunda, N. (1987) · Physical Review A · doi:10.1103/physreva.36.3868 · Cited by 266 · see citing works
Self-citationMethods for reliable teleportation
Vaidman, L., & Yoran, N. (1999) · Physical Review A · doi:10.1103/physreva.59.116 · Cited by 253 · see citing works
Quantum error correction for communication with linear optics
Braunstein, S. L. (1998) · Nature · doi:10.1038/27850 · Cited by 199 · see citing works
Gaussian pure states in quantum mechanics and the symplectic group
Simon, R., Sudarshan, E. C. G., & Mukunda, N. (1988) · Physical Review A · doi:10.1103/physreva.37.3028 · Cited by 140 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Quantum information with continuous variables
Braunstein, S. L., & van Loock, P. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.77.513 · Cited by 3,858 · see citing works
Entanglement 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
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Continuous Variable Quantum Information: Gaussian States and Beyond
Adesso, G., Ragy, S., & Lee, A. R. (2014) · Open Systems & Information Dynamics · doi:10.1142/s1230161214400010 · Cited by 787 · 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
The local approach to quantum transport may violate the second law of thermodynamics
Levy, A., & Kosloff, R. (2014) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/107/20004 · Cited by 286 · see citing works
Entanglement detection in the stabilizer formalism
Tóth, G., & Gühne, O. (2005) · Physical Review A · doi:10.1103/physreva.72.022340 · Cited by 281 · see citing works
Propagation of entangled light pulses through dispersing and absorbing channels
Chizhov, A. V., Schmidt, E., Knöll, L., & Welsch, D.-G. (2001) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/3/3/301 · Cited by 9 · see citing works
- Authors
- Simon, R.
- Affiliations
- Institute of Mathematical Sciences (IN)
- Corresponding author
- Simon, R.
- ORCID
- Simon, R.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-03-20
- Volume
- 84
- Issue
- 12
- Pages
- 2726-2729
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2161482522
- Cited by
- 2,245
- References
- 16
- Citations by year
- 2026: 81 · 2025: 134 · 2024: 93 · 2023: 153 · 2022: 119 · 2021: 118 · 2020: 128 · 2019: 96 · 2018: 81 · 2017: 101 · 2016: 88 · 2015: 93 · 2014: 66 · 2013: 81 · 2012: 69
- FWCI
- 49.62
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- Peres-Horodecki criterion, separability, continuous-variable systems, partial transposition, specular reflection, phase space, uncertainty principle, Gaussian states, bipartite states, quantum entanglement
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
