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Quantum Information Processing

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01-04-2021

Proving the distillability problem of two-copy \(4\times 4\) Werner states for monomial matrices

Authors: Lin Chen, Huixia He, Xian Shi, Li-Jun Zhao

Published in: Quantum Information Processing | Issue 4/2021

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Abstract

The distillability conjecture of two-copy \(4\times 4\) Werner states is one of the main open problems in quantum information (https://arxiv.org/abs/2002.03233, P. Horodecki, L. Rudnicki, and K. Zyczkowski). We prove three special cases of the conjecture in terms of the \(4\times 4\) non-normal matrices A, B involved in the conjecture. The first case, namely the main result of this paper, occurs when A, B are monomial matrices. Then, we apply it to the remaining two cases. One case occurs when A, B both have at most two nonzero entries. The other case works for rank-one A and some rank-two B. Our results present the latest progress on the conjecture.

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Title: Proving the distillability problem of two-copy Werner states for monomial matrices
Authors: Lin Chen
Huixia He
Xian Shi
Li-Jun Zhao
Publication date: 01-04-2021
Publisher: Springer US
Published in: Quantum Information Processing / Issue 4/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-021-03098-w

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