dorsal/arxiv
View SchemaProbabilities from Entanglement, Born's Rule from Envariance
| Authors | W. H. Zurek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405161 |
| URL | https://arxiv.org/abs/quant-ph/0405161 |
| DOI | 10.1103/PhysRevA.71.052105 |
| Journal | Phys. Rev. A 71, 052105 (2005) |
Abstract
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like'' states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Born's rule, $p_k \propto |\psi_k|^2$ for the outcomes associated with Schmidt states. Probabilities derived in this manner are an objective reflection of the underlying state of the system -- they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge'' of the observer. Envariance - based approach is compared with and found superior to pre-quantum definitions of probability including the {\it standard definition} based on the `principle of indifference' due to Laplace, and the {\it relative frequency approach} advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Born's rule: Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {\it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence. Envariant origin of Born's rule for probabilities sheds a new light on the relation between ignorance (and hence, information) and the nature of quantum states.
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"abstract": "I show how probabilities arise in quantum physics by exploring implications\nof {\\it environment - assisted invariance} or {\\it envariance}, a recently\ndiscovered symmetry exhibited by entangled quantum systems. Envariance of\nperfectly entangled ``Bell-like\u0027\u0027 states can be used to rigorously justify\ncomplete ignorance of the observer about the outcome of any measurement on\neither of the members of the entangled pair. For more general states,\nenvariance leads to Born\u0027s rule, $p_k \\propto |\\psi_k|^2$ for the outcomes\nassociated with Schmidt states. Probabilities derived in this manner are an\nobjective reflection of the underlying state of the system -- they represent\nexperimentally verifiable symmetries, and not just a subjective ``state of\nknowledge\u0027\u0027 of the observer. Envariance - based approach is compared with and\nfound superior to pre-quantum definitions of probability including the {\\it\nstandard definition} based on the `principle of indifference\u0027 due to Laplace,\nand the {\\it relative frequency approach} advocated by von Mises. Implications\nof envariance for the interpretation of quantum theory go beyond the derivation\nof Born\u0027s rule: Envariance is enough to establish dynamical independence of\npreferred branches of the evolving state vector of the composite system, and,\nthus, to arrive at the {\\it environment - induced superselection (einselection)\nof pointer states}, that was usually derived by an appeal to decoherence.\nEnvariant origin of Born\u0027s rule for probabilities sheds a new light on the\nrelation between ignorance (and hence, information) and the nature of quantum\nstates.",
"arxiv_id": "quant-ph/0405161",
"authors": [
"W. H. Zurek"
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"doi": "10.1103/PhysRevA.71.052105",
"journal_ref": "Phys. Rev. A 71, 052105 (2005)",
"title": "Probabilities from Entanglement, Born\u0027s Rule from Envariance",
"url": "https://arxiv.org/abs/quant-ph/0405161"
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