dorsal/arxiv
View SchemaDistinguishability and Accessible Information in Quantum Theory
| Authors | Christopher A. Fuchs |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9601020 |
| URL | https://arxiv.org/abs/quant-ph/9601020 |
Abstract
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in quantum cryptography and quantum computation theory. The results reported include the following. An exact expression for the quantum fidelity between two mixed states is derived. The optimal measurement that gives rise to it is studied in detail. Several upper and lower bounds on the quantum mutual information are derived via similar techniques and compared to each other. Of note is a simple derivation of the important upper bound first proved by Holevo and an explicit expression for another (tighter) upper bound that appears implicitly in the same derivation. Several upper and lower bounds to the quan- tum Kullback relative information are derived. The measures developed are also applied to ferreting out the extent to which quantum systems must be disturbed by information gathering measurements. This is tackled in two ways. The first is in setting up a general formalism for describing the tradeoff between inference and disturbance. The main point of this is that it gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures. The second result on this theme is a theorem that prohibits "broadcasting" an unknown (mixed) quantum state. That is to say, there is no way to replicate an unknown quantum state onto two separate quantum systems when each system is considered without regard to the other. This includes the possibility of correlation or quantum entanglement between the systems. This result is a significant extension and generalization of the standard "no-cloning" theorem for pure states.
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"abstract": "This document focuses on translating various information-theoretic measures\nof distinguishability for probability distributions into measures of distin-\nguishability for quantum states. These measures should have important appli-\ncations in quantum cryptography and quantum computation theory. The results\nreported include the following. An exact expression for the quantum fidelity\nbetween two mixed states is derived. The optimal measurement that gives rise to\nit is studied in detail. Several upper and lower bounds on the quantum mutual\ninformation are derived via similar techniques and compared to each other. Of\nnote is a simple derivation of the important upper bound first proved by Holevo\nand an explicit expression for another (tighter) upper bound that appears\nimplicitly in the same derivation. Several upper and lower bounds to the quan-\ntum Kullback relative information are derived. The measures developed are also\napplied to ferreting out the extent to which quantum systems must be disturbed\nby information gathering measurements. This is tackled in two ways. The first\nis in setting up a general formalism for describing the tradeoff between\ninference and disturbance. The main point of this is that it gives a way of\nexpressing the problem so that it appears as algebraic as that of the problem\nof finding quantum distinguishability measures. The second result on this theme\nis a theorem that prohibits \"broadcasting\" an unknown (mixed) quantum state.\nThat is to say, there is no way to replicate an unknown quantum state onto two\nseparate quantum systems when each system is considered without regard to the\nother. This includes the possibility of correlation or quantum entanglement\nbetween the systems. This result is a significant extension and generalization\nof the standard \"no-cloning\" theorem for pure states.",
"arxiv_id": "quant-ph/9601020",
"authors": [
"Christopher A. Fuchs"
],
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"title": "Distinguishability and Accessible Information in Quantum Theory",
"url": "https://arxiv.org/abs/quant-ph/9601020"
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