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arXiv:1901.01373 · Physical Review A

Arbitrary two-particle high-dimensional Bell-state measurement by auxiliary entanglement

Hao Zhang, Chao Zhang, Xiao‐Min Hu, Bi‐Heng Liu, Yun‐Feng Huang, Chuan‐Feng Li, Guang‐Can Guo

Published May 2, 2019• 37 citations
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Abstract

Bell-state measurements (BSMs) play a vital role in quantum information. However, there is no definite solution of how to realize high-dimensional Bell-state measurements (HDBSMs). In this paper, we present a scheme for realizing arbitrary high-dimensional two-particle BSMs by auxiliary entanglement. In our scheme, the maximally entangled states with different degrees of freedom are used as auxiliary states, and then the HDBSM can be achieved by implementing a Bell measurement with different degrees of freedom. We present the detailed HDBSM scheme for three- and four-dimensional Bell states, and the general formula for arbitrary high-dimensional Bell states. Furthermore, we design an experimental scheme for three-dimensional BSM, and give a method of arbitrary dimension. This method can promote the high-dimensional quantum information task.

DOI
10.1103/physreva.99.052301

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Bell-state measurements (BSMs) play a vital role in quantum information. However, there is no definite solution of how to realize high-dimensional Bell-state measurements (HDBSMs). In this paper, we present a scheme for realizing arbitrary high-dimensional two-particle BSMs by auxiliary entanglement. In our scheme, the maximally entangled states with different degrees of freedom are used as auxiliary states, and then the HDBSM can be achieved by implementing a Bell measurement with different degrees of freedom. We present the detailed HDBSM scheme for three- and four-dimensional Bell states, and the general formula for arbitrary high-dimensional Bell states. Furthermore, we design an experimental scheme for three-dimensional BSM, and give a method of arbitrary dimension. This method can promote the high-dimensional quantum information task.
We present a theoretical scheme for the complete Bell state measurement (BSM) for high-dimensional hyperentangled photons in polarization and path degrees of freedom (DOFs), in which the polarization entanglement is in two-dimensional Hilbert space and the path entanglement is in four-dimensional Hilbert space. This 2×4-dimensional photonic quantum system contains 64 mutually orthogonal high-dimensional hyperentangled Bell states, which can be unambiguously discriminated by using weak cross-Kerr nonlinearity, linear optical element, and single-photon detector. This is the first complete BSM scheme for high-dimensional hyperentangled photons in two DOFs assisted by the quantum nonlinear effect, and we also demonstrate its application in the quantum superdense coding protocol, which allows the transmission of log 2 64=6 bits of classical information via just sending one photon. Moreover, our scheme only requires the achievable small nonlinear phase shift, and it can provide new avenues for other BSM-based quantum information technologies involving photonic high-dimensional hyperentanglement.
With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.
We theoretically propose a simple and efficient scheme for the complete analysis of high-dimensional Bell states in N dimensions. The mutually orthogonal high-dimensional entangled states can be unambiguously distinguished by obtaining the parity and relative phase information of entanglement independently. Based on this approach, we present the physical realization of photonic four-dimensional Bell state measurement with the current technology. The proposed scheme will be useful for quantum information processing tasks that utilize high-dimensional entanglement.
Bell state measurement (BSM) plays an important role in quantum information processing. However, a complete BSM cannot be achieved with linear optics with current technology. In this paper, we present a scheme for realizing single-photon BSM via a one-dimensional photonic quantum random walk. In our scheme, the maximally entangled states with polarization and path degrees of freedom are used as Bell states; then a complete BSM based on quantum random walk can be implemented in single-photon Hilbert space. Detecting single-photon count at different positions can provide unambiguous discrimination of all four Bell states to verify our scheme. Furthermore, we also discuss how to apply our BSM scheme to the proposed single-photon cryptography system.
The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.
We theoretically investigate the distinguishability of a set of mutually orthogonal four-dimensional Bell states of photon system in path degree of freedom using only linear optics, resorting to the two-photon interference. With quantum interference effect, we find that the 16 four-dimensional Bell states can be classified into 7 groups, which can support the transmission of log27=2.81log_2 7 = 2.81log2​7=2.81 bits classical information with just sending one photon in the quantum superdense coding protocol. When an auxiliary two-dimensional polarization entanglement is introduced, the 16 four-dimensional Bell states then can be classified into 12 groups, which can promote the channel capacity to log212=3.58log_2 12 = 3.58log2​12=3.58 bits with encoding one photon. Our results are significant for photonic superdense coding, and can be useful for other quantum information technologies involved linear-optical high-dimensional Bell state measurement.