Operationally classical simulation of quantum states

• URL: http://arxiv.org/abs/2502.01440v1
• Date: Mon, 03 Feb 2025 15:25:03 GMT
• Title: Operationally classical simulation of quantum states
• Authors: Gabriele Cobucci, Alexander Bernal, Martin J. Renner, Armin Tavakoli,
• Abstract summary: A classical state-preparation device cannot generate superpositions and hence its emitted states must commute.<n>We show that no such simulation exists, thereby certifying quantum coherence.<n>Our approach is a possible avenue to understand how and to what extent quantum states defy generic models based on classical devices.
• Score: 41.94295877935867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A classical state-preparation device cannot generate superpositions and hence its emitted states must commute. Building on this elementary observation, we introduce a notion of operationally classical models in which many such devices can be stochastically coordinated for the purpose of simulating quantum states. This leads to many non-commuting quantum state ensembles admitting a classical model. We develop systematic methods both for classically simulating quantum ensembles and for showing that no such simulation exists, thereby certifying quantum coherence. In particular, we determine the exact noise rates required to classically simulate the entire state space of quantum theory. We also reveal connections between the operational classicality of ensembles and the well-known fundamental concepts of joint measurability and Einstein-Podolsky-Rosen steering. Our approach is a possible avenue to understand how and to what extent quantum states defy generic models based on classical devices, which also has relevant implications for quantum information applications.

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