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Chinese Physics B

Direct measurement of the concurrence of hybrid entangled state based on parity check measurements

Man Zhang, Lan Zhou, Wei Zhong, Yu‐Bo Sheng

Published Jan 1, 2019• 11 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/28/1/010301

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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 propose a protocol for directly measuring the concurrence of a two-qubit electronic pure entangled state. To complete this task, we first design a parity-check measurement (PCM) which is constructed by two polarization beam splitters (PBSs) and a charge detector. By using the PCM for three rounds, we can achieve the concurrence by calculating the total probability of picking up the odd parity states from the initial states. Since the conduction electron may be a good candidate for the realization of quantum computation, this protocol may be useful in future solid quantum computation.
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.
Hyperentanglement is the quantum system entangled in several degrees of freedom (DOFs), which has attracted extensive attention in quantum communication. In the practical application of hyperentanglement, the key step is to know the information of the hyperentanglement. In this paper, we propose an efficient protocol to measure the concurrence of arbitrary two-photon six-qubit hyperentangled state, which simultaneously entangles in the polarization and double longitudinal momentum DOFs. This protocol requires the weak cross-Kerr nonlinearity and some linear optical elements to construct the quantum nondemolition detection gate. The concurrence in each DOF can be converted into the success probability of distilling some specified states. Our protocol may play an important role in future quantum information processing.
It has been found that logic-qubit entanglement has great potential for applications in quantum communication and quantum networks in recent years. However, along with the effects of noise and decoherence, the fidelity of the communication transmission can be greatly reduced. In this paper, we investigate the entanglement purification of logic bit-flip error and phase-flip error in polarization logic-qubit entanglement based on the parity-check measurement (PCM) gate, which is constructed by the cross-Kerr nonlinearity and used to distinguish the parity information of two-photon polarization states. The probability of entanglement purification is higher than the scheme using the linear optical method. Moreover, the quality of logic-qubit entangled states can be improved by a cyclic purification process. This entanglement purification protocol will be useful in the future when faced with long-distance communication with logic-qubit entanglement states.
We propose an efficient protocol for measuring the concurrence of arbitrary two-photon pure entangled state with the help of the photonic Faraday rotation. In the protocol, the concurrence of the photonic entangled state can be conversed into the total success probability for picking up the odd-parity photonic state. For completing the measurement task, we require some auxiliary three-level atoms, which are trapped in the low-quality cavities. Our protocol can be well realized under current experimental conditions. Moreover, under practical imperfect atom state detection and photonic Faraday rotation conditions, our protocol can also work well. Based on these features, our protocol may be useful in current quantum information processing.
Abstract We propose an efficient method to construct an optical four-photon |χ〉 state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ〉 states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ〉 state.