| Issue |
EPL
Volume 148, Number 3, November 2024
|
|
|---|---|---|
| Article Number | 38002 | |
| Number of page(s) | 7 | |
| Section | Quantum information | |
| DOI | https://doi.org/10.1209/0295-5075/ad8bee | |
| Published online | 13 November 2024 | |
Quantum nonlocality of density operators and their corresponding density matrices
1 China People's Police University - Guangzhou 510663, China
2 School of Mathematics and Statistics, Shaanxi Normal University - Xi'an 710119, China
3 T&R office of Mathematics, Army Academy of Border and Coastal Defence - Xi'an 710108, China
Received: 25 July 2024
Accepted: 28 October 2024
Quantum nonlocality represents correlations between subsystems of a composite quantum system, usually including Bell nonlocality, steerability, and entanglement. According to the hypothesis of quantum mechanics, states of a quantum system Q described by a d-dimensional Hilbert space 
are denoted by density operators acting on . Under a basis e for the Hilbert space 
, every abstract density operator ρ of the system AB corresponds to a density matrix ρe, which is a state of the 
complex Hilbert space 
. In this work, we discuss the consistency of quantum nonlocality of density operators ρ and their corresponding density matrices ρe under the chosen basis e. It is proved that only when a basis e is a product one, a density operator ρ is entangled (respectively, Bell nonlocal, steerable) if and only if its density matrix ρe is entangled (respectively, Bell nonlocal, steerable).
© 2024 The author(s)
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