Details
| Original language | English |
|---|---|
| Article number | 022310 |
| Journal | Physical Review A |
| Volume | 94 |
| Issue number | 2 |
| Publication status | Published - 10 Aug 2016 |
| Externally published | Yes |
Abstract
Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems ABC, by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics
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In: Physical Review A, Vol. 94, No. 2, 022310, 10.08.2016.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Operational meaning of quantum measures of recovery
AU - Cooney, Tom
AU - Hirche, Christoph
AU - Morgan, Ciara
AU - Olson, Jonathan P.
AU - Seshadreesan, Kaushik P.
AU - Watrous, John
AU - Wilde, Mark M.
N1 - Funding Information: We are grateful to Mario Berta, Omar Fawzi, and Marco Tomamichel for discussions and for sharing an early draft of their work. We also thank Patrick Hayden for discussions. C.H. was supported by the Spanish MINECO, Project No. FIS2013-40627-P, as well as by the Generalitat de Catalunya, CIRIT Project No. 2014 SGR 966. J.W. was supported in part by Canada's NSERC. M.M.W. acknowledges support from the NSF under Award No. CCF-1350397.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems ABC, by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.
AB - Several information measures have recently been defined that capture the notion of recoverability. In particular, the fidelity of recovery quantifies how well one can recover a system A of a tripartite quantum state, defined on systems ABC, by acting on system C alone. The relative entropy of recovery is an associated measure in which the fidelity is replaced by relative entropy. In this paper we provide concrete operational interpretations of the aforementioned recovery measures in terms of a computational decision problem and a hypothesis testing scenario. Specifically, we show that the fidelity of recovery is equal to the maximum probability with which a computationally unbounded quantum prover can convince a computationally bounded quantum verifier that a given quantum state is recoverable. The quantum interactive proof system giving this operational meaning requires four messages exchanged between the prover and verifier, but by forcing the prover to perform actions in superposition, we construct a different proof system that requires only two messages. The result is that the associated decision problem is in QIP(2) and another argument establishes it as hard for QSZK (both classes contain problems believed to be difficult to solve for a quantum computer). We finally prove that the regularized relative entropy of recovery is equal to the optimal type II error exponent when trying to distinguish many copies of a tripartite state from a recovered version of this state, such that the type I error is constrained to be no larger than a constant.
UR - http://www.scopus.com/inward/record.url?scp=84983376009&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.94.022310
DO - 10.1103/PhysRevA.94.022310
M3 - Article
AN - SCOPUS:84983376009
VL - 94
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 2
M1 - 022310
ER -