On quantum advantage in dense coding

Horodecki, Michał; Piani, Marco

doi:10.1088/1751-8113/45/10/105306

Cited by 53 publications

(48 citation statements)

References 33 publications

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“…Dense coding is a procedure where A sends her subsystem to B, and by doing so she is able to transmit more classical information than she could if the system is classical. In the most general dense-coding scenario (Horodecki et al, 2001;Horodecki and Piani, 2012;Winter, 2002), A encodes her message by means of general quantum operations (Λ A ⊗ I B )[ρ AB ] = ρ A B , and the quantum operation changes the dimension of…”

Section: Dense-coding Capacitymentioning

confidence: 99%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

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One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformation-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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Section: Dense-coding Capacitymentioning

confidence: 99%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

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“…Again, a quantum state is said to be dense codeable if the above quantity (A B) is strictly positive. It was shown in the paper by Horodecki [31] that it suffices to consider only the extremal TPCP maps in evaluating the infimum or supremum for the above quantity, owing to the concavity of the von Neumann entropy. It was also shown that the quantum advantage of dense coding may be nonadditive, although not proved definitely.…”

Section: Implications On the Quantum Advantage Of Dense Codingmentioning

confidence: 99%

“…It was shown to be satisfying the properties of a genuine measure of total correlation. Also, a monogamy relation involving the entanglement of purification and the quantum advantage of dense coding was given by Horodecki et al [31]. However, the conditions for the monogamy or polygamy nature of entanglement of purification have not been found yet.…”

Section: Introductionmentioning

confidence: 99%

Monogamy, polygamy, and other properties of entanglement of purification

Bagchi

Pati

2015

Phys. Rev. A

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For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.Comment: 12 pages, 2 figures, Published versio

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“…Achieving this in a cheap and reliable way is essential to the development of future quantum technologies. They also reinforces the role of quantum discord as a beneficial and practically relevant quantity [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]: as discord appears to bound the entanglement gain and to allow for excessive entanglement distribution, it emerges as a key player of fundamental relevance in the context of quantum communication and networking.…”

Section: Discussionmentioning

confidence: 52%

Excessive distribution of quantum entanglement

et al. 2016

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We classify protocols of entanglement distribution as excessive and non-excessive ones. In a non-excessive protocol, the gain of entanglement is bounded by the amount of entanglement being communicated between the remote parties, while excessive protocols violate such bound. We first present examples of excessive protocols that achieve a significant entanglement gain. Next we consider their use in noisy scenarios, showing that they improve entanglement achieved in other ways and for some situations excessive distribution is the only possibility of gaining entanglement.

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On quantum advantage in dense coding

Cited by 53 publications

References 33 publications

The classical-quantum boundary for correlations: Discord and related measures

The classical-quantum boundary for correlations: Discord and related measures

Monogamy, polygamy, and other properties of entanglement of purification

Excessive distribution of quantum entanglement

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