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arXiv:2009.11539 · Physical Review A

Quantum state rotation: Circularly transferring quantum states of multiple users

Yonghae Lee, Hayata Yamasaki, Soojoon Lee

Published Jun 22, 2021• 4 citations
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Abstract

Quantum state exchange is a quantum communication task for two users in which the users faithfully exchange their respective parts of an initial state under the asymptotic scenario. In this work, we generalize the quantum state exchange task to a quantum communication task for $M$ users in which the users circularly transfer their respective parts of an initial state. We assume that every pair of users may share entanglement resources, and they use local operations and classical communication in order to perform the task. We call this generalized task the (asymptotic) quantum state rotation. First of all, we formally define the quantum state rotation task and its optimal entanglement cost, which means the least amount of total entanglement required to carry out the task. We then present lower and upper bounds on the optimal entanglement cost, and provide conditions for zero optimal entanglement cost. Based on these results, we find out a difference between the quantum state rotation task for three or more users and the quantum state exchange task.

DOI
10.1103/physreva.103.062613

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Quantum state exchange is a quantum communication task for two users in which the users faithfully exchange their respective parts of an initial state under the asymptotic scenario. In this work, we generalize the quantum state exchange task to a quantum communication task for MMM users in which the users circularly transfer their respective parts of an initial state. We assume that every pair of users may share entanglement resources, and they use local operations and classical communication in order to perform the task. We call this generalized task the (asymptotic) quantum state rotation. First of all, we formally define the quantum state rotation task and its optimal entanglement cost, which means the least amount of total entanglement required to carry out the task. We then present lower and upper bounds on the optimal entanglement cost, and provide conditions for zero optimal entanglement cost. Based on these results, we find out a difference between the quantum state rotation task for three or more users and the quantum state exchange task.
Quantum state exchange is a quantum communication task for two users in which the users exchange their respective quantum information in the asymptotic scenario. In this work, we generalize the quantum state exchange task to a quantum communication task for MMM users in which the users rotate their respective quantum information. We assume that every two users may share entanglement resources, and they use local operations and classical communication in order to perform the task. We call this generalized task the quantum state rotation. First of all, we formally define the quantum state rotation task and its optimal entanglement cost, which means the least amount of total entanglement resources required to carry out the task. We then present lower and upper bounds on the optimal entanglement cost, and provide conditions for zero optimal entanglement costs. Based on these results, we find out a difference between the quantum state rotation task and the quantum state exchange task.
Quantum state exchange is a quantum communication task in which two users exchange their respective quantum information in the asymptotic setting. In this paper, 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 study how the users deal with their symmetric information in order to reduce the entanglement cost. Moreover, we show that it is possible for the users to gain extra shared entanglement after this task.
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.
Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms. In this Letter we study the role of quantum coherence for quantum state redistribution, a fundamental task where two parties aim to relocate a quantum particle by using a limited amount of quantum communication and shared entanglement. We provide general bounds for the resource rates required for this process, and show that these bounds are tight under additional reasonable constraints, including the situation where the receiving party cannot use local coherence. While entanglement cannot be directly converted into local coherence in our setting, we show that entanglement is still useful for local coherence creation if an additional quantum channel is provided, and the optimal protocol for local coherence creation for any given amount of quantum communication and shared entanglement is presented. We also discuss possible extensions of our methods to other scenarios where the receiving party is limited by local constraints, including theories of thermodynamics and asymmetry.
Suppose that two distant parties Alice and Bob share an entangled state ρAB\rho_{AB}ρAB​, and they want to exchange the subsystems of ρAB\rho_{AB}ρAB​ by local operations and classical communication (LOCC). In general, this LOCC task (i.e. the LOCC transformation of ρAB→VρABV\rho_{AB} \to V\rho_{AB} VρAB​→VρAB​V with VVV being a swap operator) is impossible deterministically, but becomes possible probabilistically. In this paper, we study how the optimal probability is related to the amount of entanglement in the framework of positive partial transposed (PPT) operations, and numerically show a remarkable class of states whose probability is the smallest among every state in two quantum bits.
If two parties share an unknown quantum state, one can ask how much quantum communication is needed for party A to send her share to party B. Recently, it was found that the number of qubits which should be sent is given by the conditional entropy. This quantifies the notion of partial information, and it can even be negative. Here, we not only demand that A send her state to B, but additionally, B should send his state to A. Paradoxically, we find that requiring that the parties perform this additional task can lower the amount of quantum communication required. This primitive, which we call quantum state exchange, can be used to quantify the notion of uncommon information, since the two parties only need to send each other the parts of their state they don't hold in common. In the classical case, the concept of uncommon information follows trivially from the concept of partial information. We find that for quantum states, this is not so. We prove upper and lower bounds for the uncommon information and find optimal protocols for several classes of states.