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Entropy

Concurrence Measurement for the Two-Qubit Optical and Atomic States

Lan Zhou, Yu‐Bo Sheng

Published Jun 19, 2015• 35 citations
Publisher

Abstract

Concurrence provides us an effective approach to quantify entanglement, which is quite important in quantum information processing applications. In the paper, we mainly review some direct concurrence measurement protocols of the two-qubit optical or atomic system. We first introduce the concept of concurrence for a two-qubit system. Second, we explain the approaches of the concurrence measurement in both a linear and a nonlinear optical system. Third, we introduce some protocols for measuring the concurrence of the atomic entanglement system.

DOI
10.3390/e17064293

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Concurrence provides us an effective approach to quantify entanglement, which is quite important in quantum information processing applications. In the paper, we mainly review some direct concurrence measurement protocols of the two-qubit optical or atomic system. We first introduce the concept of concurrence for a two-qubit system. Second, we explain the approaches of the concurrence measurement in both a linear and a nonlinear optical system. Third, we introduce some protocols for measuring the concurrence of the atomic entanglement system.
Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely, concurrence, of an arbitrary two-qubit pure state via a single fixed measurement setup by exploiting so-called weak measurements and the associated weak values together with the properties of the Laguerre-Gaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol.
This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.
Abstract Concurrence is an important parameter for quantifying quantum entanglement, but usually the state tomography must be determined before quantification. In this paper we propose a scheme, based on cavity-assisted atom–light interaction, to measure the concurrence of two-atom pure states and the Collins–Gisin state directly, without tomography. The concurrence of atomic states is encoded in the output coherent optical beams after interacting with cavities and the atoms therein, so the results of detection applied to the output coherent optical beams provide the concurrence data of the atomic states. This scheme provides an alternative method for directly measuring atomic entanglement by detecting coherent light, rather than measuring the atomic systems, which thus greatly simplifies the realization complexity of the direct measurement of atomic entanglement. In addition, as the cavity-assisted atom–light interaction used here is robust and scalable in realistic applications, the current scheme may be realized in the near future.
The hybrid entangled state is widely discussed in quantum information processing. In this paper, we propose the first protocol to directly measure the concurrence of the hybrid entangled state. To complete the measurement, we design parity check measurements (PCMs) for both the single polarization qubit and the coherent state. In this protocol, we perform three rounds of PCMs. The results show that we can convert the concurrence into the success probability of picking up the correct states from the initial entangled states. This protocol only uses polarization beam splitters, beam splitters, and weak cross-Kerr nonlinearities, which is feasible for future experiments. This protocol may be useful in future quantum information processing.
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.