Measuring higher-dimensional entanglement

Abstract

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems -- qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental set ups can be used to measure the entanglement using our scheme.

7 pages, 2 figures

References in corpus (9)

• Efficient quantum state tomography
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Noise robustness of the nonlocality of entangled quantum states
• Characterization of high-dimensional entangled systems via mutually unbiased measurements
• Non-Locality of Experimental Qutrit Pairs
• Experimental violation of Bell inequalities for multi-dimensional systems
• Gisin's theorem for two d-dimensional systems based on the Collins-Gisin-Linden-Masser-Popescu inequality
• Fourier Transform Quantum State Tomography
• A Few Finite Trigonometric Sums

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• Generation and Detection of Quantum Correlations and Entanglement on a Spin-Based Quantum Information Processor