Indiscernibility of quantum states

• URL: http://arxiv.org/abs/2507.10027v1
• Date: Mon, 14 Jul 2025 08:07:06 GMT
• Title: Indiscernibility of quantum states
• Authors: Jan van Neerven, Marijn Waaijer,
• Abstract summary: We argue that, given a set of observables, the distinguishable objects'' are the equivalence classes modulo indiscernibility relative to the observables.<n>The structure of the set of distinguishable objects - called the Holevo space - is investigated in detail.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we develop a mathematical framework for indiscernibility of quantum states, arguing that, given a set of observables, the ``distinguishable objects'' are the equivalence classes modulo indiscernibility relative to the observables. The structure of the set of distinguishable objects - called the Holevo space - is investigated in detail, and it is shown that the observables admit a natural lift to continuous functions on the Holevo space. The theory is illustrated by several examples where the ``distinguishable objects'' can be described explicitly. Among other things, the Holevo spaces and the lifted functions are described for position measurements on a free particle and for spin measurements in the EPR and Bell experiments.

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