Commuting operations factorise


Date

2023-08-10

Publication Type

Working Paper

ETH Bibliography

yes

Citations

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Data

Abstract

Consider two agents, Alice and Bob, each of whom takes a quantum input, operates on a shared quantum system $K$, and produces a quantum output. Alice and Bob's operations may commute, in the sense that the joint input-output behaviour is independent of the order in which they access $K$. Here we ask whether this commutation property implies that $K$ can be split into two factors on which Alice and Bob act separately. The question can be regarded as a "fully quantum" generalisation of a problem posed by Tsirelson, who considered the case where Alice and Bob's inputs and outputs are classical. In this case, the answer is negative in general, but it is known that a factorisation exists in finite dimensions. Here we show the same holds in the fully quantum case, i.e., commuting operations factorise, provided that all input systems are finite-dimensional.

Publication status

published

Editor

Book title

Journal / series

Volume

Pages / Article No.

2308.05792

Publisher

Cornell University

Event

Edition / version

v1

Methods

Software

Geographic location

Date collected

Date created

Subject

Quantum Physics (quant-ph); Mathematical Physics (math-ph); FOS: Physical sciences

Organisational unit

03781 - Renner, Renato / Renner, Renato check_circle

Notes

Funding

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