Efficient bounds on quantum-communication rates via their reduced variants

Abstract

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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