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Energy-Constrained LOCC-Assisted Quantum Capacity of the Bosonic Dephasing Channel

by Amir Arqand, Laleh Memarzadeh and Stefano Mancini

Entropy 2023, 25(7), 1001; https://doi.org/10.3390/e25071001 - 29 Jun 2023

Cited by 4 | Viewed by 1432

We study the LOCC-assisted quantum capacity of a bosonic dephasing channel with energy constraint on the input states. We start our analysis by focusing on the energy-constrained squashed entanglement of the channel, which is an upper bound for the energy-constrained LOCC-assisted quantum capacity. As computing energy-constrained squashed entanglement of the channel is challenging due to a double optimization (over the set of density matrices and the isometric extensions of a squashing channel), we first derive an upper bound for it, and then, we discuss how tight that bound is for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel. In doling so, we prove that the optimal input state is diagonal in the Fock basis. Then, we analyze two explicit examples of squashing channels through which we derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel in terms of its quantum capacity with different noise parameters. As the difference between upper and lower bounds becomes smaller by increasing the dephasing parameter, the bounds become tighter. Full article

(This article belongs to the Section Quantum Information)

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15 pages, 492 KiB

Open AccessArticle

Correlations in Quantum Network Topologies Created with Cloning

by Manish Kumar Shukla, Minyi Huang, Indranil Chakrabarty and Junde Wu

Mathematics 2023, 11(11), 2440; https://doi.org/10.3390/math11112440 - 25 May 2023

Cited by 1 | Viewed by 1546

Abstract

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which will help us to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in situations wherever the availability of entangled pairs is limited. In addition to that, we focus on the problem of distinguishing networks created by cloning from those that are created by distributing independently generated entangled pairs. We find that there are several states that cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article, we use tripartite mutual information to distinguish cloned networks from networks created by independent sources and further use squashed entanglement as a measure to quantify the amount of dependence in the cloned networks. Full article

(This article belongs to the Special Issue Quantum Algorithms and Relative Problems)

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