Entanglement Cost of Optimal Distributed Quantum State Purification

Abstract:We determine the preshared entanglement required for spatially separated parties, restricted to local operations and classical communication, to attain globally optimal probabilistic two-copy purification of arbitrary bipartite pure states under depolarizing noise. In every local dimension $d\ge 2$, one shared maximally entangled qubit pair suffices: local controlled-SWAP operations exactly reproduce the globally optimal successful transformation. Conversely, any finite-dimensional preshared resource state that attains the same benchmark, even under a positive-partial-transpose relaxation, must have entanglement of formation at least one ebit. For pure resources with one ebit, or for two-qubit resources including mixed states, attaining the benchmark is possible only for states with exactly two nonzero Schmidt weights, both equal to $1/2$, namely those locally unitarily equivalent to a maximally entangled qubit pair. These findings provide a benchmark for evaluating the entanglement demands of noise management in quantum networks and modular quantum computers.

arXiv:2609.23441 [quant-ph]

(or arXiv:2609.23441v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23441 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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