Separation of quantum, spatial quantum, and approximate quantum correlations

Salman Beigi

QuOne Lab, Phanous Research and Innovation Centre, Tehran, Iran

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Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{q}$}}^{(4, 4, 2,2)} \neq \mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 2,2)}$. We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, $\textit{i.e.}$, $\mathcal{C}_{\text{$\rm{qs}$}}^{(4, 4, 3,3)} \neq \mathcal{C}_{\text{$\rm{qa}$}}^{(4, 4, 3,3)}$.

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Cited by

[1] Shubhayan Sarkar and Remigiusz Augusiak, "Self-testing of multipartite Greenberger-Horne-Zeilinger states of arbitrary local dimension with arbitrary number of measurements per party", Physical Review A 105 3, 032416 (2022).

[2] Connor Paddock, William Slofstra, Yuming Zhao, and Yangchen Zhou, "An Operator-Algebraic Formulation of Self-testing", Annales Henri Poincaré (2023).

[3] Shubhayan Sarkar, "Certification of entangled quantum states and quantum measurements in Hilbert spaces of arbitrary dimension", arXiv:2302.01325, (2023).

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