Asymptotic Compressibility of Entanglement and Classical Communication in Distributed Quantum Computation

Abstract

We consider implementations of a bipartite unitary on many pairs of unknown input states by local operation and classical communication assisted by shared entanglement. We investigate to what extent the entanglement cost and the classical communication cost can be compressed by allowing nonzero but vanishing error in the asymptotic limit of infinite pairs. We show that a lower bound on the minimal entanglement cost, the forward classical communication cost, and the backward classical communication cost per pair is given by the Schmidt strength of the unitary. We also prove that an upper bound on these three kinds of the cost is given by the amount of randomness that is required to partially decouple a tripartite quantum state associated with the unitary. In the proof, we construct a protocol in which quantum state merging is used. For generalized Clifford operators, we show that the lower bound and the upper bound coincide. We then apply our result to the problem of distributed compression of tripartite quantum states, and derive a lower and an upper bound on the optimal quantum communication rate required therein.

Section II and VIII added

References in corpus (13)

• On the quantum, classical and total amount of correlations in a quantum state
• One-shot decoupling
• The decoupling approach to quantum information theory
• On the efficiency of nonlocal gates generation
• Quantum state redistribution based on a generalized decoupling
• State redistribution as merging: introducing the coherent relay
• Entanglement requirements for implementing bipartite unitary operations
• Local implementation of nonlocal operations of block forms
• On the distributed compression of quantum information
• Implementation of multipartite unitary operations with limited resources
• Relation between classical communication capacity and entanglement capability for two-qubit unitary operations
• All maximally entangling unitary gates
• Lower bounds for communication capacities of two-qudit unitary operations

Cited by in corpus (1)

• A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation