The Linear Optical Unambiguous Discrimination of Hyperentangled Bell States Assisted by Time Bin

Abstract

A linear optical unambiguous discrimination of hyperentangled Bell states is proposed for two-photon systems entangled in both the polarization and momentum degrees of freedom (DOFs) assisted by time bin. This unambiguous discrimination scheme can completely identify 16 orthogonal hyperentangled Bell states using only linear optical elements, where the function of the auxiliary entangled Bell state is replaced by time bin. Moreover, the possibility of extending this scheme for distinguishing hyperentangled Bell states in n DOFs is discussed, and it shows that 2 n+k+1 hyperentangled Bell states in n (n ≥ 2) DOFs can be distinguished with k (k < n) auxiliary entangled states of additional DOFs by introducing a time delay, which decreases the auxiliary entanglement resource required for unambiguous discrimination of hyperentangled Bell state. Therefore, this scheme provides a new way for distinguishing hyperentangled states with current technology, which will extend the application of discrimination of hyperentangled states via linear optics to other quantum information protocols besides hyperdense coding schemes in the future. IntroductionPhoton system is one of the most interesting candidates for quantum communication with the character of manipulability, high-speed transmission, and high capacity. The entangled photon system is a crucial quantum resource in quantum communication, which has many important applications in quantum communication protocols, such as quantum key distribution, [1][2][3][4] quantum secret sharing, [5] quantum dense coding, [6,7] quantumThe ORCID identification number(s) for the author(s) of this article can be found under https://doi.

Deterministic and complete hyperentangled Bell states analysis assisted by frequency and time interval degrees of freedom

“…In our scheme, the 16 hyper-Bell states are distinguished unambiguously. One fixed momentum (spatial) entangled state and one time-bin DOF are employed by Gao et al [44] to complete momentum-(spatial-) polarization HBSA. One fixed momentum (spatial) entangled state and one fixed frequency entangled state are employed by Wang et al [56] to complete momentum-(spatial-) polarization HBSA.…”

“…In 2017, Li et al [43] showed that 4 n hyper-Bell states can be separated into 2 n+k+1 −2 2k distinct groups via linear optics with help of k (k ≤ n) additional entangled states in ancillary DOFs. In 2019, Gao et al [44] proved that 2 n+k+1 hyper-Bell states in n (n ≥ 2) DOFs can be distinguished via linear optics with help of a time delay and k (k ≤ n) auxiliary entangled states in additional DOFs. In 2020, Gao et al [45] further enhanced to 14 distinct groups only assisted by time-bin DOF.…”

“…[56,57]. In addition, frequency DOF is much more insensitive to the channel noise in an optical fiber than spatial (momentum) and polarization DOFs [44,56,57].…”

Complete Hyperentangled Bell States Analysis For Polarization‐Spatial‐Time‐Bin Degrees of Freedom with Unity Fidelity

“…[37] Tremendous progress has also been made in hyperentangled Bell states analysis (HBSA). [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] In 2007, Wei et al [48] shown that 16 hyperentangled Bell (hyper-Bell) states cannot be unambiguously distinguished only using linear optics. Later, the first complete HBSA scheme was proposed by Sheng et al [49] in 2010 via cross-Kerr nonlinearity, and another interesting HBSAs via cross-Kerr nonlinearity were proposed later.…”

Complete hyperentangled Bell states analysis for polarization-spatial-time-bin degrees of freedom with unity fidelity

“…Tremendous progress has also been made in hyperentangled Bell states analysis (HBSA). [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] In 2007, Wei et al [48] shown that 16 hyperentangled Bell (hyper-Bell) states can not be unambiguously distinguished only using linear optics. Later, the first complete HBSA scheme was proposed by Sheng et al [49] in 2010 via cross-Kerr nonlinearity, and another interesting HBSAs via cross-Kerr nonlinearity were proposed later.…”