Steerability criteria based on Heisenberg-Weyl observables. (English) Zbl 1520.81021
Summary: Einstein-Podolsky-Rosen (EPR) steering is an intermediate form of nonlocality which interpolates between entanglement and Bell nonlocality. It has been shown that EPR steerable states are fundamental resources for one-sided device-independent quantum information tasks. Nevertheless, distinguishing quantum steerable states from the unsteerable ones in general cases remains a big challenge under active studies. The generalized Bloch representation of density matrices in terms of the Heisenberg observables is a useful tool for analyzing characteristics of quantum systems and plays an important role in quantum information. In this work, the role of this representation in detection of EPR steering is studied. More specifically, based on the correlation matrices of the Heisenberg-Weyl observables, a family of steerability criteria for arbitrary dimensional bipartite systems are proposed. A large class of Hermitian operators, which can conveniently witness steering in some scenarios, are further provided. Finally, these criteria are illustrated through several examples, are compared with some existing ones, and their power and advantages are exhibited in certain cases.
MSC:
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 30H30 | Bloch spaces |
Keywords:
EPR steering; Heisenberg-Weyl observables; correlation matrices; generalized Bloch representationReferences:
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