A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation

Abstract

We analyze implementations of bipartite unitaries by means of local operations and classical communication (LOCC) assisted by shared entanglement. We employ concepts and techniques developed in quantum Shannon theory to study an asymptotic scenario, in which two distant parties perform the same bipartite unitary on infinitely many pairs of inputs. We analyze minimum cost of entanglement and classical communication per copy. For two-round LOCC protocols, we derive a single-letter formula for the minimum cost of entanglement and classical communication, under an additional requirement that the error converges to zero faster than $1/n^4$, where $n$ is the number of input pairs. The formula is given by the "Markovianizing cost" of a tripartite state associated with the unitary, which can be computed by a finite-step algorithm. We also derive a lower bound on the minimum cost of resources, which applies for protocols with arbitrary number of rounds.

32 pages, 8 figures

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Cited by in corpus (13)

• Fundamental limits on the capacities of bipartite quantum interactions
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
• Deconstruction and conditional erasure of quantum correlations
• Universal limitations on implementing resourceful unitary evolutions
• Conditional Decoupling of Quantum Information
• Complexity of causal order structure in distributed quantum information processing and its trade-off with entanglement
• State exchange with quantum side information
• One-Shot Randomized and Nonrandomized Partial Decoupling
• Quantum State Merging for Arbitrarily Small-Dimensional Systems
• Distributed Encoding and Decoding of Quantum Information over Networks
• One-Shot Triple-Resource Trade-Off in Quantum Channel Coding
• The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation