Entanglement estimation in non-optimal qubit states

Abstract

In the last years, a relationship has been established between the quantum Fisher information (QFI) and quantum entanglement. In the case of two-qubit systems, all pure entangled states can be made useful for sub-shot-noise interferometry while their QFI meets a necessary and sufficient condition [1]. In M-qubit systems, the QFI provides just a sufficient condition in the task of detecting the degree of entanglement of a generic state [2]. In our work, we show analytically that, for a large class of one-parameter non-optimal two-qubit states, the maximally entangled states are associated with stationary points of the QFI, as a function of such parameter. We show, via numerical simulations, that this scenario is maintained for the generalisation of this class of states to a generic M-qubit system. Furthermore, we suggest a scheme for an interferometer able to detect the entanglement in a large class of two-spin states.

arXiv comment7 pages, 7 figures

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• Entanglement, Non-linear Dynamics, and the Heisenberg Limit
• Not all pure entangled states are useful for sub shot-noise interferometry
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Cited by in corpus (4)

• Entanglement and Quantum Correlation Measures from a Minimum Distance Principle
• Entanglement distance for arbitrary $M$-qudit hybrid systems
• Entanglement distance for an arbitrary state of M qubits
• Unveiling the geometric meaning of quantum entanglement: discrete and continuous variable systems