On the Entanglement Cost of One-Shot Compression
Shima Bab Hadiashar, Ashwin Nayak

TL;DR
This paper investigates the fundamental limits of quantum state compression with entanglement assistance in a one-shot setting, revealing cases where entanglement is essential and can drastically reduce communication costs.
Contribution
It demonstrates that shared entanglement can significantly lower communication costs in quantum compression, and constructs ensembles that saturate known bounds even with relaxed protocols.
Findings
Shared entanglement reduces communication cost arbitrarily.
Certain ensembles are incompressible without entanglement.
Entanglement can be more resource-efficient than classical communication.
Abstract
We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complexity, we lift certain restrictions that are placed on compression protocols in tasks such as state-splitting and channel simulation. We show that an ensemble of the form designed by Jain, Radhakrishnan, and Sen (ICALP'03) saturates the known bounds on the sum of communication and entanglement…
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