Indistinguishability of identical bosons from a quantum information theory perspective

• URL: http://arxiv.org/abs/2307.06626v1
• Date: Thu, 13 Jul 2023 08:45:51 GMT
• Title: Indistinguishability of identical bosons from a quantum information theory perspective
• Authors: Matthias Englbrecht, Tristan Kraft, Christoph Dittel, Andreas Buchleitner, Geza Giedke, Barbara Kraus
• Abstract summary: We present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability. We show that these states are diagonal in the computational basis up to a permutationally invariant unitary.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Using tools from quantum information theory, we present a general theory of indistinguishability of identical bosons in experiments consisting of passive linear optics followed by particle number detection. Our results do neither rely on additional assumptions on the input state of the interferometer, such as, for instance, a fixed mode occupation, nor on any assumption on the degrees of freedom that potentially make the particles distinguishable. We identify the expectation value of the projector onto the $N$-particle symmetric subspace as an operationally meaningful measure of indistinguishability, and derive tight lower bounds on it that can be efficiently measured in experiments. Moreover, we present a consistent definition of perfect distinguishability and characterize the corresponding set of states. In particular, we show that these states are diagonal in the computational basis up to a permutationally invariant unitary. Moreover, we find that convex combinations of states that describe partially distinguishable and perfectly indistinguishable particles can lead to perfect distinguishability, which itself is not preserved under convex combinations.

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