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arXiv:1203.1512 · Europhysics Letters (EPL)

Macroscopic observables detecting genuine multipartite entanglement and partial inseparability in many-body systems

A. Gabriel, Beatrix C. Hiesmayr

Published Feb 1, 2013• 10 citations
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Abstract

We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum computation, our methods can be used to select or design appropriate condensed matter systems.

DOI
10.1209/0295-5075/101/30003

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Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges for systems like time-bin encoded qubits and microwave photons from superconducting circuits, where qubit connectivity is limited or measurement noise grows with the number of jointly measured qubits. Here we introduce versatile GME and k-inseparability criteria applicable to any state, which only require measuring O(n2) out of 2n (at most) m-body stabilizers of n-qubit target graph states, with m upper-bounded by twice the graph’s maximum degree. For cluster or ring-graph states, only constant-weight stabilizers are needed. Using semidefinite programming (and sometimes graph-local complementations), we can reduce the number or weight of required stabilizers. Analytical and numerical results show that our criteria are noise-robust and may infer state infidelity from certified k-inseparability in microwave photonic graph states generated under realistic conditions.
We investigate a priori detection probabilities of genuine multipartite entanglement (GME). Even if one does not have knowledge of the basis in which a state is produced by a source, how a channel decoheres it or of the very working of the detectors used, we find that it is possible to detect GME with reasonably high probability in a feasible fashion. We show that by means of certain separability criteria, GME can be detected in a measurement-base-independent way. Our method provides several applications whenever e.g. state tomography is not possible or too demanding, and is a tool to investigate security issues in multi-particle quantum cryptographical protocols.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.
Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy nnn-partite W state when n=3,4,5n = 3, 4, 5n=3,4,5 and 666, and find that the criterion can detect more noisy W states when nnn ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of 333-qutrit state. The result is stronger than that based on GME concurrence and fisher information.