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Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.


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TL;DR: In this article, the authors employ non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime.
Abstract: The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that one-way information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during information reconciliation is not generally valid. We propose an improved approximation that takes into account finite key effects and numerically test it against codes for two probability distributions, that we call binary-binary and binary-Gaussian, that typically appear in quantum key distribution protocols.

11 citations

Journal ArticleDOI
TL;DR: In this paper, the degree of irreducible multiparty correlations in a multiparty quantum state based on quantum relative entropy is defined and shown to be equivalent to those derived from the maximal von Neumann entropy principle.
Abstract: Generalizing Amari's work titled "Information geometry on hierarchy of probability distributions" [IEEE Trans. Inf. Theory 47, 1701 (2001)], we define the degrees of irreducible multiparty correlations in a multiparty quantum state based on quantum relative entropy. We prove that these definitions are equivalent to those derived from the maximal von Neumann entropy principle [Phys. Rev. Lett. 89, 207901 (2002) and Phys. Rev. Lett. 101, 180505 (2008)]. Based on these definitions, we find a counterintuitive result on irreducible multiparty correlations: although the degree of the total correlation in a three-party quantum state does not increase under local operations, irreducible three-party correlations can be created by local operations from a three-party state with only irreducible two-party correlations. In other words, even if a three-partite state is initially completely determined by measuring two-party Hermitian operators, the determination of the state after local operations has to resort to the measurements of three-party Hermitian operators.

11 citations

Posted Content
TL;DR: In this paper, it was shown that the finiteness of the output entropy of a positive linear map on the whole input state space implies its continuity, and sufficient conditions for this property expressed in terms of the Kraus representation of quantum channels and operations were presented.
Abstract: Continuity properties of the output entropy of positive linear maps between Banach spaces of trace class operators are investigated with the special attention to the classes of quantum channels and operations. It is shown that finiteness of the output entropy of a positive map on the whole input state space implies its continuity. Sufficient conditions for this property expressed in terms of the Kraus representation of quantum channels and operations are presented. The characterization of a positive map "preserving continuity of the entropy" (in the sense that continuity of the entropy on a set of input states implies continuity of its output entropy on this set) is obtained and its applications to the class of quantum operations are considered. The special relation between continuity properties of the output entropies of complementary quantum operations is established and its corollaries are discussed. Continuity conditions for the output entropy of positive maps considered as a function of a pair (map, input state) are also obtained. Several applications to the quantum information theory are presented in the last part of the paper.

11 citations

Journal ArticleDOI
TL;DR: Using graph state basis, it is shown that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable.
Abstract: Quantum capacities of Pauli channels are not additive, a degenerate quantum code may improve the hashing bound of the capacity. The difficulty in approaching the capacity is how to calculate the coherent information of a generic degenerate quantum code. Using graph state basis, we greatly reduce the problem for the input of quantum error-correcting code. We show that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable. When the input state is an equal probable mixture of codewords of a stabilizer code, the coherent information can be analytically obtained.

11 citations

Journal ArticleDOI
TL;DR: In this article, the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality has been shown to provide substantial advantages.
Abstract: We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH nonlocality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly nonclassical states of bosonic systems.

11 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20234
202211
202122
202017
201923
201818