dorsal/arxiv
View SchemaEssentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated
| Authors | Paul B. Slater |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9909062 |
| URL | https://arxiv.org/abs/quant-ph/9909062 |
| DOI | 10.1088/1464-4266/2/4/101 |
| Journal | J. Opt. B: Quantum Semiclass. Opt. 2 (2000) L19-L24 |
Abstract
Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon (quant-ph/9909044) have recently found necessary and sufficient conditions for the separability (classical correlation) of the Gaussian two-party (continuous variable) states. Duan et al remark that their criterion is based on a "much stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type operators than is required simply by the uncertainty relation. Here, we seek to formalize and test this particular assertion in both classical and quantum-theoretic frameworks. We first attach to these states the classical a priori probability (Jeffreys' prior), proportional to the volume element of the Fisher information metric on the Riemannian manifold of Gaussian (quadrivariate normal) probability distributions. Then, numerical evidence indicates that more than ninety-nine percent of the Gaussian two-party states do, in fact, meet the more stringent criterion for separability. We collaterally note that the prior probability assigned to the classical states, that is those having positive Glauber-Sudarshan P-representations, is less than one-thousandth of one percent. We, then, seek to attach as a measure to the Gaussian two-party states, the volume element of the associated (quantum-theoretic) Bures (minimal monotone) metric. Our several extensive analyses, then, persistently yield probabilities of separability and classicality that are, to very high orders of accuracy, unity and zero, respectively, so the two apparently quite distinct (classical and quantum-theoretic) forms of analysis are rather remarkably consistent in their findings.
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"abstract": "Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon\n(quant-ph/9909044) have recently found necessary and sufficient conditions for\nthe separability (classical correlation) of the Gaussian two-party (continuous\nvariable) states. Duan et al remark that their criterion is based on a \"much\nstronger bound\" on the total variance of a pair of Einstein-Podolsky-Rosen-type\noperators than is required simply by the uncertainty relation. Here, we seek to\nformalize and test this particular assertion in both classical and\nquantum-theoretic frameworks. We first attach to these states the classical a\npriori probability (Jeffreys\u0027 prior), proportional to the volume element of the\nFisher information metric on the Riemannian manifold of Gaussian (quadrivariate\nnormal) probability distributions. Then, numerical evidence indicates that more\nthan ninety-nine percent of the Gaussian two-party states do, in fact, meet the\nmore stringent criterion for separability. We collaterally note that the prior\nprobability assigned to the classical states, that is those having positive\nGlauber-Sudarshan P-representations, is less than one-thousandth of one\npercent. We, then, seek to attach as a measure to the Gaussian two-party\nstates, the volume element of the associated (quantum-theoretic) Bures (minimal\nmonotone) metric. Our several extensive analyses, then, persistently yield\nprobabilities of separability and classicality that are, to very high orders of\naccuracy, unity and zero, respectively, so the two apparently quite distinct\n(classical and quantum-theoretic) forms of analysis are rather remarkably\nconsistent in their findings.",
"arxiv_id": "quant-ph/9909062",
"authors": [
"Paul B. Slater"
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"quant-ph"
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"doi": "10.1088/1464-4266/2/4/101",
"journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 2 (2000) L19-L24",
"title": "Essentially All Gaussian Two-Party Quantum States are a priori Nonclassical but Classically Correlated",
"url": "https://arxiv.org/abs/quant-ph/9909062"
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