A simple test for quantum channel capacity

Nowakowski, Marcin; Horodecki, Paweł

doi:10.1088/1751-8113/42/13/135306

Cited by 15 publications

(29 citation statements)

References 37 publications

(63 reference statements)

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“…One could note that it might be useful to partition the set of all symmetric extendible states SE by relation of k-extendibility. If S k denotes a convex set [18] of all states being k-extendible, there holds the natural inclusion relation [ Fig. 1]:…”

Section: Symmetric Extendible Statesmentioning

confidence: 99%

The symmetric extendibility of quantum states

Nowakowski¹

2016

J. Phys. A: Math. Theor.

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Studies on symmetric extendibility of quantum states become especially important in a context of analysis of one-way quantum measures of entanglement, distilabillity and security of quantum protocols. In this paper we analyse composite systems containing a symmetric extendible part with a particular attention devoted to one-way security of such systems. Further, we introduce a new oneway monotone based on the best symmetric approximation of quantum state. We underpin those results with geometric observations on structures of multi-party settings which posses in sub-spaces substantial symmetric extendible components. Finally, we state a very important conjecture linking symmetric-extendibility with one-way distillability and security of all quantum states analyzing behavior of private key in neighborhood of symmetric extendible states.

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Section: Symmetric Extendible Statesmentioning

confidence: 99%

The symmetric extendibility of quantum states

Nowakowski¹

2016

J. Phys. A: Math. Theor.

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“…Originally introduced as a test for entanglement [9], symmetric extendibility has a number of operational interpretations. For example, a symmetrically extendible state cannot be used for one-way entanglement distillation [10] or one-way secret key distillation [11]. The relationship between symmetric extendibility and Bell nonlocality has also been studied; the results of Ref.…”

Section: Chsh Violation and Symmetric Extendibilitymentioning

confidence: 99%

Quantum correlations of two-qubit states with one maximally mixed marginal

et al. 2014

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We investigate the entanglement, CHSH nonlocality, fully entangled fraction and symmetric extendibility of two-qubit states that have a single maximally mixed marginal. Within this set of states, the steering ellipsoid formalism has recently highlighted an interesting family of so-called 'maximally obese' states. These are found to have extremal quantum correlation properties that are significant in the steering ellipsoid picture and for the study of two-qubit states in general.

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“…The following examples will show application of the concept: Example 1. As an example of application of Theorem 2 we present a state which after discarding a small B' part on Bob's side becomes a symmetric extendible state [18]. This example is especially important since the presented state does not possess [19] any symmetric extendible component in its decomposition for symmetric and non-symmetric parts, thus, one cannot use the method [20] to find an upper bound on K → by means of linear optimization.…”

Section: S(ρ Bbmentioning

confidence: 99%

“…This matrix is represented in the computational basis |00 , |01 , |10 , |11 held by Alice and Bob and possess a singlet-like structure. Whenever one party (Alice or Bob) measures the state, the state decoheres and off-diagonal elements vanish which leads to a symmetric extendible state [18]:…”

Section: S(ρ Bbmentioning

confidence: 99%

Efficient bounds on quantum-communication rates via their reduced variants

Nowakowski

Horodecki

2010

Phys. Rev. A

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We investigate one-way communication scenarios where Bob manipulating on his parts can transfer some sub-system to the environment. We define reduced versions of quantum communication rates and further, prove new upper bounds on one-way quantum secret key, distillable entanglement and quantum channel capacity by means of their reduced versions. It is shown that in some cases they drastically improve their estimation.PACS numbers: 03.67.Hk Recently years have seen enormous advances in quantum information theory proving it has been well established as a basis for a concept of quantum computation and communication. Much work [1][2][3][4][5][6][7] has been performed to understand how to operate on quantum states and distill entanglement enabling quantum data processing or establish quantum secure communication between two or more parties. One of the central problems of quantum communication field is to estimate efficiency of communication protocols establishing secure communication between involved parties or distilling quantum entanglement [5][6][7][8][9][10][11]. Most simple communication scenarios are those that do not use classical side channel or use it only in one-way setup. The challenge for the present theory is to determine good bounds on such quantities like the secret key rate or quantum channel capacity and distillable entanglement of a quantum state, that allow to estimate the communication capabilities. In this paper we provide efficient upper bounds avoiding massive overestimation of communication rates. We are inspired by classical information and entanglement measures theory where so-called reduced quantities have been used [8,10,12]. Herewith we consider two pairs of quantities: private capacity P, quantum one-way secret key K → and one-way quantum channel capacity Q → , one-way distillable entanglement D → providing new efficient upper bounds. We prove that in some cases the bounds explicitly show that the corresponding quantity is relatively small if compared to sender and receiver systems. The main method is again the fact that all the above quantities vanish on some classes of systems. Moreover, we introduce 'defect' parameters ∆ for the reduced quantities resulting from possible transfer of sub-systems on receivers' side which are (sub)additive and hence, can be exploited in case of composite systems and regularization.Reduced one-way secret key. A secret key is a quantum resource allowing two parties Alice and Bob private communication over a public channel. In an ideal scenario they generate a pair of maximally correlated classical secure bit-strings such that Eve representing the * Electronic address: pawel@mif.pg.gda.pl adversary in the communication is not able to receive any sensible information from further communication between Alice and Bob. In this section we will elaborate on generation of a one-way secret key from a tripartite quantum state shared by the parties with Eve that means Alice and Bob can use only protocols consisting of local operations and one-way public communicat...

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A simple test for quantum channel capacity

Cited by 15 publications

References 37 publications

The symmetric extendibility of quantum states

The symmetric extendibility of quantum states

Quantum correlations of two-qubit states with one maximally mixed marginal

Efficient bounds on quantum-communication rates via their reduced variants

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