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Quantum measurement incompatibility in subspaces

Kraft, Tristan
Miklin, Nikolai
Pellonpää, Juha-Pekka
Gühne, Otfried
Published in Physical review, A, Atomic, molecular, and optical physics. 2021, vol. 103, no. 022203
Abstract We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is incompatible, one considers the set of measurements obtained by projection onto any strict subspace of fixed dimension. We identify three possible forms of incompatibility in subspaces: (i) incompressible incompatibility: measurements that become compatible in every subspace, (ii) fully compressible incompatibility: measurements that remain incompatible in every subspace, and (iii) partly compressible incompatibility: measurements that are compatible in some subspace and incompatible in another. For each class we discuss explicit examples. Finally, we present some applications of these ideas. First we show that joint measurability and coexistence are two inequivalent notions of incompatibility in the simplest case of qubit systems. Second we highlight the implications of our results for tests of quantum steering.
arXiv: 2010.04048
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Research group Groupe Brunner
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UOLA, Roope Kristian et al. Quantum measurement incompatibility in subspaces. In: Physical Review. A, 2021, vol. 103, n° 022203. doi: 10.1103/PhysRevA.103.022203 https://archive-ouverte.unige.ch/unige:150406

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Deposited on : 2021-03-15

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