Abstract
The quantum state exchange is a quantum communication task in which two users exchange their respective quantum information in the asymptotic setting. In this work, we consider a one-shot version of the quantum state exchange task, in which the users hold a single copy of the initial state, and they exchange their parts of the initial state by means of entanglement-assisted local operations and classical communication. We first derive lower bounds on the least amount of entanglement required for carrying out this task, and provide conditions on the initial state such that the protocol succeeds with zero entanglement cost. Based on these results, we reveal two counter-intuitive phenomena in this task, which make it different from a conventional SWAP operation. One tells how the users deal with their symmetric information in order to reduce the entanglement cost. The other shows that it is possible for the users to gain extra shared entanglement after this task.
Highlights
In quantum information theory, 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 real number r is called a converse bound of the optimal entanglement cost if it is upper bounded by the entanglement cost of any one-shot quantum state exchange (OSQSE) protocol
In Proposition 3, the first inequality comes from the fact that Alice and Bob cannot increase the amount of entanglement between them by means of LOCC [26], while the second one is straightforward from the definitions of the optimal entanglement costs
Summary
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. It is not easy in a realistic situation to prepare a sufficiently large number of state copies, and the amount of nonlocal resources available for the users is limited To reflect these practical difficulties, quantum information research has focused more recently on the one-shot scenario [9,10,11,12,13,14,15,16,17]. We introduce and study the one-shot quantum state exchange (OSQSE) task. This is a useful quantum communication task, but can have a potential application in quantum computation.
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