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arXiv:1602.04852 · Physical Review A

Experimental measurement of collective nonlinear entanglement witness for two qubits

Karel Lemr, Karol Bartkiewicz, Antonín Černoch

Published Nov 28, 2016• 20 citations
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Abstract

We present a proof-of-principle experiment demonstrating measurement of the collectibility, a nonlinear entanglement witness proposed by \L{}. Rudnicki et al. [Phys. Rev. Lett. 107, 150502 (2011)]. This entanglement witness works for both mixed and pure two-qubit states. In the latter case it can be used to measure entanglement in terms of the negativity. We measured the collectibility for three distinct classes of photonic polarization-encoded two-qubit states, i.e., maximally entangled, separable, and maximally mixed states. We demonstrate that the measurement procedure is feasible and robust against typical experimental shortcomings such as imperfect two-photon indistinguishability.

DOI
10.1103/physreva.94.052334

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We present a proof-of-principle experiment demonstrating measurement of the collectibility, a nonlinear entanglement witness proposed by \L{}. Rudnicki et al. [Phys. Rev. Lett. 107, 150502 (2011)]. This entanglement witness works for both mixed and pure two-qubit states. In the latter case it can be used to measure entanglement in terms of the negativity. We measured the collectibility for three distinct classes of photonic polarization-encoded two-qubit states, i.e., maximally entangled, separable, and maximally mixed states. We demonstrate that the measurement procedure is feasible and robust against typical experimental shortcomings such as imperfect two-photon indistinguishability.
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Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is extended here for mixed quantum states. We define collectibility for any mixed states of a multipartite system. Deriving bounds for collectibility for positive partially transposed states of given purity provides insight into the structure of entangled quantum states. In the case of two qubits the application of complementary measurements and coincidence based detections leads to a test of entanglement of pseudopure states.
We experimentally demonstrate a method for detection of entanglement via construction of entanglement witnesses from a limited fixed set of local measurements ( M ). Such a method does not require a priori knowledge about the form of the entanglement witnesses. It is suitable for a scenario where a full state tomography is not available, but the only resource is a limited set of M . We demonstrate the method on pure two-qubit entangled states and mixed two-qubit entangled states, which emerge from photonic implementation of controllable quantum noisy channels. The states we select are motivated by realistic experimental conditions, and we confirm it works well for both cases. Furthermore, possible generalizations to higher-dimensional bipartite systems have been considered, which can potentially detect both decomposable and indecomposable entanglement witnesses. Our experimental results show perfect validity of the method, which indicates that even a limited set of local measurements can be used for quick entanglement detection and further provide a practical test bed for experiments with entanglement witnesses.
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We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.
We describe a classical model that may serve as an analog for joint and local measurements of an entanglement witness. The analogous experimental procedure and data analysis protocol of the model follow those of a previous experiment to measure an entanglement witness with polarized photons prepared in a mixed state [Phys. Rev. Lett. 91, 227901 (2003)]. Numerical simulations show excellent agreement with both experimental results and quantum-mechanical predictions. This agreement is made possible by the fact that the model exhibits contextuality due to the postselection of coincident detection events.