preprints.org > physical sciences > quantum science and technology > doi: 10.20944/preprints202404.1505.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 22 April 2024 / Approved: 23 April 2024 / Online: 23 April 2024 (08:52:07 CEST)

Quantum nonlocality represents correlation properties between subsystems of a composite quantum system, usually including the four types: Bell nonlocality, steerability, entanglement, and quantum correlation (quantum discord). Given a basis $e_{AB}=\{|e_{ij}\>\}_{i\in[d_A],j\in[d_B]}$ for the Hilbert space $\H_A\otimes \H_B$ of a bipartite system $AB$, a density operator $\rho^{AB}$ (quantum state) of $AB$ can be represented as a $d_Ad_B\times d_Ad_B$ matrix $\hat{\rho}_{e_{AB}}=[\]$, called the density matrix of a density operator $\rho^{AB}$. A natural question is what is the relationship between the quantum nonlocality of a density operator $\rho^{AB}$ and its corresponding density matrix $\hat{\rho}_{e_{AB}}$? In this work, we discuss the relationships between quantum locality and basis, and prove that one type of quantum locality of density operators and that of their density matrices under a basis are the same if and only if the chosen basis is the tensor product of the bases of subsystems. Consequently, different bases define different quantum nonlocality density operators.

basis-dependence; density operator; density matrix; classical correlation; separability; unsteerability; Bell locality

Physical Sciences, Quantum Science and Technology

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