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arXiv:1801.02851 · Scientific Reports

Entanglement criterion independent on observables for multipartite Gaussian states based on uncertainty principle

Kan He, Miaomiao Huang, Jinchuan Hou

Published Feb 4, 2019• 1 citation
arXivHTMLPDF

Abstract

Quantum entanglement is one of important resources for quantum communication. Entanglement criteria help us detect entangled states. One of important criteria is the local uncertainty relation (LUR) entanglement criteria, which is studied extensively. However, all existent LUR criteria are dependent on the chosen observables. In the paper, applying the uncertainty principle, we improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.

DOI
10.1038/s41598-018-36307-1

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Quantum entanglement is one of important resources for quantum communication. Entanglement criteria help us detect entangled states. One of important criteria is the local uncertainty relation (LUR) entanglement criteria, which is studied extensively. However, all existent LUR criteria are dependent on the chosen observables. In the paper, applying the uncertainty principle, we improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.
We propose a sufficient criterion for the entanglement of tripartite systems based on local sum uncertainty relations for arbitrarily chosen observables of subsystems. This criterion generalizes the tighter criterion for bipartite systems introduced by Zhang et al. [C.-J. Zhang, H. Nha, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 81, 012324 (2010)] and can be used for both discrete- and continuous-variable systems. It enables us to detect the entanglement of quantum states without having a complete knowledge of them. Its utility is illustrated by some examples of three-qubit, qutrit-qutrit-qubit, and three-mode Gaussian states. It is found that, in comparison with other criteria, this criterion is able to detect some three-qubit bound entangled states more efficiently.
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.
Multipartite entanglement detection is crucial for the develop of quantum information science and quantum computation, communication, simulation and metrology tasks. In contrast to experiments, where several handreds of qubits have been entangled to build a quantum computer or a quantum simulator, theoretically only for lower dimensional quantum system such as two qubit system or two-mode Gaussian state and some special quantum states, efficient criteria have been developed to detect the entanglement. An efficient and practical entanglement detection method is anticipated to appear for current scalable quantum system. Based on the matched entanglement witness scheme and integrated uncertainty relations, we propose a quite general entanglement detection method for all kinds of multipartite entanglement of multimode continuous variable systems. With the covariance matrix of any randomly generated multimode continuous variable quantum state, our criterion can detect entanglement, genuine entanglement and other kinds of inseparabilities almost imidiately.
Entanglement for continuous variable states opens up an avenue for experimental utilization of the entanglement properties of quantum physics very easily. Non- Gaussian continuous variable state improves the efficiency and robustness of a quantum teleportation and communication. Thus, it is important to understand the entanglement properties of non-Gaussian states. For a class of non-Gaussian continuous variable states, we derive a general criterion for SU(2) operators which incidentally coincides with the work of Agarwal and Biswas and another entanglement criteria for SU(1,1) operators for a two-mode non-Gaussian state using uncertainty relation and Cauchy-Schwarz inequality.