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Updated: Jun 10, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Published on: September 8, 2023

Commuting Quantum Operations Factorise.

Renato Renner1,2, Ramona Wolf3

  • 1Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland.

Communications in Mathematical Physics
|June 9, 2026
PubMed
Summary
This summary is machine-generated.

Commuting quantum operations on a shared system factorize, allowing separate actions by agents Alice and Bob. This holds true when all input systems are finite-dimensional, extending a classical problem to quantum mechanics.

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Area of Science:

  • Quantum Information Theory
  • Quantum Computing
  • Mathematical Physics

Background:

  • Investigates the relationship between commuting operations and system factorization in quantum mechanics.
  • Extends Tsirelson's problem, originally concerning classical inputs/outputs, to a fully quantum setting.
  • Explores the implications of order-independent operations on a shared quantum system.

Purpose of the Study:

  • To determine if commuting quantum operations imply a factorization of the shared quantum system.
  • To generalize Tsirelson's problem to scenarios with quantum inputs and outputs.
  • To analyze the conditions under which a shared quantum system can be decomposed for separate agent operations.

Main Methods:

  • Formal analysis of quantum operations and system factorization.
  • Mathematical framework for commuting operations in a shared quantum system.
  • Extension of classical Tsirelson problem to quantum domain.

Main Results:

  • Demonstrates that commuting quantum operations do indeed imply system factorization.
  • Shows that this factorization holds in the fully quantum case, analogous to finite-dimensional classical cases.
  • Establishes the condition of finite-dimensional input systems for this factorization property.

Conclusions:

  • Commutation of quantum operations guarantees system factorization when input systems are finite-dimensional.
  • Confirms that the property of factorizability extends from classical to quantum regimes under specific conditions.
  • Provides a significant result for understanding the structure of quantum operations and shared quantum systems.