State Exchange with Quantum Side Information

Abstract

We consider a quantum communication task between two users Alice and Bob, in which Alice and Bob exchange their respective quantum information by means of local operations and classical communication assisted by shared entanglement. Here, we assume that Alice and Bob may have quantum side information, not transferred, and classical communication is free. In this work, we derive general upper and lower bounds for the least amount of entanglement which is necessary to perfectly perform this task, called the state exchange with quantum side information. Moreover, we show that the optimal entanglement cost can be negative when Alice and Bob make use of their quantum side information. We finally provide conditions on the initial state for the state exchange with quantum side information which give the exact optimal entanglement cost. PACS numbers: 03.67.Hk, 89.70.Cf, 03.67.Mn Introduction.-In quantum information theory, one of the most traditional research topics has been source coding problems of transmitting Alice's quantum information to Bob under various situations, with paradigmatic examples including Schumacher compression [1] and quantum teleportation [2]. A decade ago, Oppenheim and Winter devised a new type of a quantum communication task named state exchange [3] -in which Alice and Bob exchange their quantum information with each other by means of local operations and classical communication (LOCC) and shared entanglement -and they studied the least amount of entanglement consumed in the task when free classical communication is allowed.In the original state exchange task, it is assumed that both Alice and Bob do not have any quantum side information (QSI) transferrable during the protocol. On the other hand, most quantum communication tasks, including state merging [4,5] and state redistribution [6,7], begin with the assumption that either Alice or Bob has QSI. For example, in the state merging task, Bob can make use of his QSI for merging Alice's information to him, and the minimum amount of entanglement needed for merging turns out to be exactly given by the quantum conditional entropy [8] conditioned on Bob's QSI.In this work we generalize in the state exchange to an exchanging task allowing Alice's and Bob's QSI, which is called the state exchange with quantum side information.

Quantum one-time tables for unconditionally secure qubit-commitment

“…Our qubit-commitment scheme, satisfying general security criteria while preserving coherence of the committed quantum state, has broad applications in the upcoming era of quantum network [38]. One example could be an implementation of a fair version of quantum state exchange [39,40]. If two quantum computers are demanded to generate certain quantum states independently and to be cross-checked afterward [41], one computer should not acquire the other's output state before generating its state.…”

Unconditionally Secure Relativistic Quantum Qubit Commitment

“…[14]. It was found that the quantum qubit commitment has some unique applications [15] beyond quantum bit commitment in the upcoming era of quantum network, including implementing a fair version of quantum state exchange [16] and preventing cheating in such a task that two quantum computers are demanded to generate certain quantum states independently and to be cross-checked afterward [17], in which one computer may try to delay to generate its state after the other party and cheat by learning from the other party's state or even try to imperfectly clone the state to pretend to have high computational power. It was also pointed out [15] that secure quantum qubit commitment can break asynchronous quantum network assumption since it can effectively activate multiple quantum machines at the same time.…”

One-shot quantum state exchange

“…Introduction.-In quantum information theory, the quantum state exchange [1,2] is a quantum communication task, in which two users, Alice and Bob, exchange their quantum information by means of local operations and classical communication (LOCC) assisted by shared entanglement. A main research aim in the study of the quantum state exchange is to evaluate the least amount of entanglement needed for the task, as in other quantum communication tasks, such as quantum state merging [3,4] and quantum state redistribution [5,6].…”

“…We formally define the OSQSE and its optimal entanglement cost, and derive computable lower bounds on the latter, which in turn yield bounds for the asymptotic quantum state exchange [1,2]. In addition, we provide two useful conditions to decide whether a given initial state enables OSQSE with zero entanglement cost.…”

“…As in the asymptotic scenario [1,2], we consider a oneshot version of the R-assisted quantum state exchange task, in which the reference system R is divided into two systems R A and R B , and then Alice and Bob receive the divided parts R A and R B , respectively, so that the initial state…”