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

doi:10.1007/s11467-022-1168-z

Front. Phys.

2022, Vol. 17

Issue (5) : 41502 https://doi.org/10.1007/s11467-022-1168-z

RESEARCH ARTICLE

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

Xin-Jie Zhou¹, Wen-Qiang Liu^1,², Hai-Rui Wei¹(

), Yan-Bei Zheng¹, Fang-Fang Du³

¹. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
². Center for Quantum Technology Research and Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements (MOE), School of Physics, Beijing Institute of Technology, Beijing 100081, China
³. Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan 030051, China

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Abstract

Hyperentangled Bell states analysis (HBSA) is an essential building block for certain hyper-parallel quantum information processing. We propose a complete and deterministic HBSA scheme encoded in spatial and polarization degrees of freedom (DOFs) of two-photon system assisted by a fixed frequency-based entanglement and a time interval DOF. The parity information the spatial-based and polarization-based hyper-entanglement can be distinguished by the distinct time intervals of the photon pairs, and the phase information can be distinguished by the detection signature. Compared with previous schemes, the number of the auxiliary entanglements is reduced from two to one by introducing time interval DOF. Moreover, the additional frequency and time interval DOFs suffer less from the collective channel noise.

Keywords hyperentangled Bell states analysis multiple degrees of freedom time interval

Corresponding Author(s): Hai-Rui Wei

Issue Date: 17 June 2022

Cite this article:

Xin-Jie Zhou,Wen-Qiang Liu,Hai-Rui Wei, et al. Deterministic and complete hyperentangled Bell states analysis assisted by frequency and time interval degrees of freedom[J]. Front. Phys. , 2022, 17(5): 41502.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1168-z
https://academic.hep.com.cn/fop/EN/Y2022/V17/I5/41502

Fig.1 Schematic diagram of the complete hyper-Bell state analysis. The frequency beam splitter (FBS) leads the photon with

ω 1

and

ω 2

into the spatial modes

x 1

and

x 2

, respectively. The frequency shifter (FS) completes the bit-flip operation on frequency DOF

X f = | ω 2 ? ? ω 1 | + | ω 1 ? ? ω 2 |

. UI is an unbalanced interferometer [45]. The circles “circle” on the path

c 1

and

d 2

introduce time intervals

t 0

and

t 1

, respectively.

H W P 22.5 °

represents a half-wave plate oriented at

22.5 °

of the horizontal direction, which completes the transformations

H p = 12 [(| H ? + | V ?) ? H | + (| H ? ? | V ?) ? V |]

on the incident photon. BS is a 50:50 beam splitter. PBS is a polarization beam splitter, which transmits the horizontally polarized component

| H ?

and reflects the vertically polarized component

| V ?

of photons.

Input	Detection	Time
states	signatures	intervals

$\| ? s + ? ? \| ? p + ?$	$a 11 H (V) b 22 V (H)$ , $a 12 H (V) b 21 V (H)$ , $b 11 H (V) a 22 V (H)$ , $b 12 H (V) a 21 V (H)$	0
$\| ? s + ? ? \| ? p ? ?$	$a 11 H (V) b 21 H (V)$ , $a 12 H (V) b 22 H (V)$ , $b 11 H (V) a 21 H (V)$ , $b 12 H (V) a 22 H (V)$
$\| ? s ? ? ? \| ? p + ?$	$a 11 H (V) a 12 H (V)$ , $a 12 H (V) a 11 H (V)$ , $a 21 H (V) a 22 H (V)$ , $a 22 H (V) a 21 H (V)$ , $b 11 H (V) b 12 H (V)$ , $b 12 H (V) b 11 H (V)$ , $b 21 H (V) b 22 H (V)$ , $b 22 H (V) b 21 H (V)$
$\| ? s ? ? ? \| ? p ? ?$	$a 11 H (V) a 11 V (H)$ , $a 12 H (V) a 12 V (H)$ , $a 21 H (V) a 21 V (H)$ , $a 22 H (V) a 22 V (H)$ , $b 11 H (V) b 11 V (H)$ , $b 12 H (V) b 12 V (H)$ , $b 21 H (V) b 21 V (H)$ , $b 22 H (V) b 22 V (H)$
$\| ψ s + ? ? \| ψ p + ?$	$a 11 H (V) b 12 H (V)$ , $a 12 H (V) b 11 H (V)$ , $a 21 H (V) b 22 H (V)$ , $a 22 H (V) b 21 H (V)$ , $a 11 H (V) a 22 V (H)$ , $a 12 H (V) a 21 V (H)$ , $b 11 H (V) b 22 V (H)$ , $b 12 H (V) b 21 V (H)$	$t 0$
$\| ψ s + ? ? \| ψ p ? ?$	$a 11 H (V) b 11 V (H)$ , $a 12 H (V) b 12 V (H)$ , $a 21 H (V) b 21 V (H)$ , $a 22 H (V) b 22 V (H)$ , $a 11 H (V) a 21 H (V)$ , $a 12 H (V) a 22 H (V)$ , $b 11 H (V) b 21 H (V)$ , $b 12 H (V) b 22 H (V)$
$\| ψ s ? ? ? \| ψ p + ?$	$a 11 H (V) a 12 H (V)$ , $a 12 H (V) a 11 H (V)$ , $a 21 H (V) a 22 H (V)$ , $a 22 H (V) a 21 H (V)$ ,
$\| ψ s ? ? ? \| ψ p + ?$	$b 11 H (V) b 12 H (V)$ , $b 12 H (V) b 11 H (V)$ , $b 21 H (V) b 22 H (V)$ , $b 22 H (V) b 21 H (V)$ , $a 11 H (V) b 22 V (H)$ , $a 12 H (V) b 21 V (H)$ , $a 21 H (V) b 12 V (H)$ , $a 22 H (V) b 11 V (H)$
$\| ψ s ? ? ? \| ψ p ? ?$	$a 11 H (V) a 11 V (H)$ , $a 12 H (V) a 12 V (H)$ , $a 21 H (V) a 21 V (H)$ , $a 22 H (V) a 22 V (H)$ ,
$\| ψ s ? ? ? \| ψ p ? ?$	$b 11 H (V) b 11 V (H)$ , $b 12 H (V) b 12 V (H)$ , $b 21 H (V) b 21 V (H)$ , $b 22 H (V) b 22 V (H)$ , $a 11 H (V) b 21 H (V)$ , $a 12 H (V) b 22 H (V)$ , $a 21 H (V) b 11 H (V)$ , $a 22 H (V) b 12 H (V)$
$\| ? s + ? ? \| ψ p + ?$	$a 11 H (V) a 12 V (H)$ , $a 12 H (V) a 11 V (H)$ , $a 21 H (V) a 22 V (H)$ , $a 22 H (V) a 21 V (H)$ ,
$\| ? s + ? ? \| ψ p + ?$	$b 11 H (V) b 12 V (H)$ , $b 12 H (V) b 11 V (H)$ , $b 21 H (V) b 22 V (H)$ , $b 22 H (V) b 21 V (H)$ , $a 11 H (V) b 22 V (H)$ , $a 12 H (V) b 21 V (H)$ , $a 21 H (V) b 12 V (H)$ , $a 22 H (V) b 11 V (H)$	$t 1$
$\| ? s + ? ? \| ψ p ? ?$	$a 11 H (V) a 11 H (V)$ , $a 12 H (V) a 12 H (V)$ , $a 21 H (V) a 21 H (V)$ , $a 22 H (V) a 22 H (V)$ ,
$\| ? s + ? ? \| ψ p ? ?$	$b 11 H (V) b 11 H (V)$ , $b 12 H (V) b 12 H (V)$ , $b 21 H (V) b 21 H (V)$ , $b 22 H (V) b 22 H (V)$ , $a 11 H (V) b 21 H (V)$ , $a 12 H (V) b 22 H (V)$ , $a 21 H (V) b 11 H (V)$ , $a 22 H (V) b 12 H (V)$
$\| ? s ? ? ? \| ψ p + ?$	$a 11 H (V) a 12 H (V)$ , $a 12 H (V) a 11 H (V)$ , $a 21 H (V) a 22 H (V)$ , $a 22 H (V) a 21 H (V)$ ,
$\| ? s ? ? ? \| ψ p + ?$	$b 11 H (V) b 12 H (V)$ , $b 12 H (V) b 11 H (V)$ , $b 21 H (V) b 22 H (V)$ , $b 22 H (V) b 21 H (V)$ , $a 11 H (V) b 22 H (V)$ , $a 12 H (V) b 21 H (V)$ , $a 21 H (V) b 12 H (V)$ , $a 22 H (V) b 11 H (V)$
$\| ? s ? ? ? \| ψ p ? ?$	$a 11 H (V) a 11 V (H)$ , $a 12 H (V) a 12 V (H)$ , $a 21 H (V) a 21 V (H)$ , $a 22 H (V) a 22 V (H)$ ,
$\| ? s ? ? ? \| ψ p ? ?$	$b 11 H (V) b 11 V (H)$ , $b 12 H (V) b 12 V (H)$ , $b 21 H (V) b 21 V (H)$ , $b 22 H (V) b 22 V (H)$ , $a 11 H (V) b 21 V (H)$ , $a 12 H (V) b 22 V (H)$ , $a 21 H (V) b 11 V (H)$ , $a 22 H (V) b 12 V (H)$
$\| ψ s + ? ? \| ? p + ?$	$a 11 H (V) a 22 H (V)$ , $a 11 H (V) a 22 V (H)$ , $a 12 H (V) a 21 H (V)$ , $a 12 H (V) a 21 V (H)$ , $b 11 H (V) b 22 H (V)$ , $b 11 H (V) b 22 V (H)$ , $b 12 H (V) b 21 H (V)$ , $b 12 H (V) b 21 V (H)$ ,
$\| ψ s + ? ? \| ? p + ?$	$a 11 H (V) b 12 H (V)$ , $a 11 H (V) b 12 V (H)$ , $a 12 H (V) b 11 H (V)$ , $a 12 H (V) b 11 V (H)$ , $a 21 H (V) b 22 H (V)$ , $a 21 H (V) b 22 V (H)$ , $a 22 H (V) b 21 H (V)$ , $a 22 H (V) b 21 V (H)$	$t 1 ± t 0$
$\| ψ s + ? ? \| ? p ? ?$	$a 11 H (V) a 21 H (V)$ , $a 11 H (V) a 21 V (H)$ , $a 12 H (V) a 22 H (V)$ , $a 12 H (V) a 22 V (H)$ , $b 11 H (V) b 21 H (V)$ , $b 12 H (V) b 22 H (V)$ , $b 11 H (V) b 21 V (H)$ , $b 12 H (V) b 22 V (H)$ ,
$\| ψ s + ? ? \| ? p ? ?$	$a 11 H (V) b 11 H (V)$ , $a 11 H (V) b 11 V (H)$ , $a 12 H (V) b 12 H (V)$ , $a 12 H (V) b 12 V (H)$ , $a 21 H (V) b 21 H (V)$ , $a 21 H (V) b 21 V (H)$ , $a 22 H (V) b 22 H (V)$ , $a 22 H (V) b 22 V (H)$
$\| ψ s ? ? ? \| ? p + ?$	$a 11 H (V) a 12 H (V)$ , $a 12 H (V) a 11 H (V)$ , $a 21 H (V) a 22 H (V)$ , $a 22 H (V) a 21 H (V)$ , $b 11 H (V) b 12 H (V)$ , $b 12 H (V) b 11 H (V)$ , $b 21 H (V) b 22 H (V)$ , $b 22 H (V) b 21 H (V)$ ,
	$a 11 H (V) b 22 H (V)$ , $a 12 H (V) b 21 H (V)$ , $a 11 H (V) b 22 V (H)$ , $a 12 H (V) b 21 V (H)$ , $a 21 H (V) b 12 H (V)$ , $a 22 H (V) b 11 H (V)$ , $a 21 H (V) b 12 V (H)$ , $a 22 H (V) b 11 V (H)$ ,
	$a 11 H (V) a 12 V (H)$ , $a 12 H (V) a 11 V (H)$ , $a 21 H (V) a 22 V (H)$ , $a 22 H (V) a 21 V (H)$ , $b 11 H (V) b 12 V (H)$ , $b 12 H (V) b 11 V (H)$ , $b 21 H (V) b 22 V (H)$ , $b 22 H (V) b 21 V (H)$
$\| ψ s ? ? ? \| ? p ? ?$	$a 11 H (V) a 11 H (V)$ , $a 11 H (V) a 11 V (H)$ , $a 12 H (V) a 12 H (V)$ , $a 12 H (V) a 12 V (H)$ , $a 21 H (V) a 21 H (V)$ , $a 21 H (V) a 21 V (H)$ , $a 22 H (V) a 22 H (V)$ , $a 22 H (V) a 22 V (H)$ ,
	$b 11 H (V) b 11 H (V)$ , $b 11 H (V) b 11 V (H)$ , $b 12 H (V) b 12 H (V)$ , $b 12 H (V) b 12 V (H)$ , $b 21 H (V) b 21 H (V)$ , $b 21 H (V) b 21 V (H)$ , $b 22 H (V) b 22 H (V)$ , $b 22 H (V) b 22 V (H)$ ,
	$a 11 H (V) b 21 H (V)$ , $a 12 H (V) b 22 H (V)$ , $a 11 H (V) b 21 V (H)$ , $a 12 H (V) b 22 V (H)$ , $a 21 H (V) b 11 H (V)$ , $a 21 H (V) b 11 V (H)$ , $a 22 H (V) b 12 H (V)$ , $a 22 H (V) b 12 V (H)$

Tab.1 Relations between the 16 hyperentangled Bell states, the detection signatures, and the time intervals. 0,

t 0

t 1

, and

t 1 ± t 0

are the time intervals of the two outing photons.

1	A. Nielsen M. L. Chuang I., Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000
2	Raussendorf R. , J. Briegel H. . A one-way quantum computer. Phys. Rev. Lett., 2001, 86( 22): 5188 https://doi.org/10.1103/PhysRevLett.86.5188
3	Raussendorf R. , E. Browne D. , J. Briegel H. . Measurement-based quantum computation on cluster states. Phys. Rev. A, 2003, 68( 2): 022312 https://doi.org/10.1103/PhysRevA.68.022312
4	Liu S. , Lou Y. , Jing J. . Orbital angular momentum multiplexed deterministic all-optical quantum teleportation. Nat. Commun., 2020, 11( 1): 3875 https://doi.org/10.1038/s41467-020-17616-4
5	Langenfeld S. , Welte S. , Hartung L. , Daiss S. , Thomas P. , Morin O. , Distante E. , Rempe G. . Quantum teleportation between remote qubit memories with only a single photon as a resource. Phys. Rev. Lett., 2021, 126( 13): 130502 https://doi.org/10.1103/PhysRevLett.126.130502
6	Ning W. , J. Huang X. , R. Han P. , Li H. , Deng H. , B. Yang Z. , Xia Y. , Xu K. , N. Zheng D. , B. Zheng S. . Deterministic entanglement swapping in a superconducting circuit. Phys. Rev. Lett., 2019, 123( 6): 060502 https://doi.org/10.1103/PhysRevLett.123.060502
7	X. Ji Z. , R. Fan P. , G. Zhang H. . Entanglement swapping for Bell states and Greenberger−Horne− Zeilinger states in qubit systems. Physica A, 2022, 585 : 126400 https://doi.org/10.1016/j.physa.2021.126400
8	H. Bennett C. , J. Wiesner S. . Communication via one- and two-particle operators on Einstein−Podolsky−Rosen states. Phys. Rev. Lett., 1992, 69( 20): 2881 https://doi.org/10.1103/PhysRevLett.69.2881
9	Guo Y. , H. Liu B. , F. Li C. , C. Guo G. . Advances in quantum dense coding. Adv. Quantum Technol., 2019, 2( 5−6): 1900011 https://doi.org/10.1002/qute.201900011
10	Wang P. , Q. Yu C. , X. Wang Z. , Y. Yuan R. , F. Du F. , C. Ren B. . Hyperentanglement-assisted hyperdistillation for hyper-encoding photon system. Front. Phys., 2022, 17 : 31501 https://doi.org/10.1007/s11467-021-1120-7
11	L. Long G. , S. Liu X. . Theoretically efficient highcapacity quantum-key-distribution scheme. Phys. Rev. A, 2002, 65( 3): 032302 https://doi.org/10.1103/PhysRevA.65.032302
12	H. Li X. , G. Deng F. , Y. Zhou H. . Efficient quantum key distribution over a collective noise channel. Phys. Rev. A, 2008, 78( 2): 022321 https://doi.org/10.1103/PhysRevA.78.022321
13	M. Liang L. , H. Sun S. , S. Jiang M. , Y. Li C. . Security analysis on some experimental quantum key distribution systems with imperfect optical and electrical devices. Front. Phys., 2014, 9 : 613 https://doi.org/10.1007/s11467-014-0420-6
14	C. W. Lim C. , Xu F. , W. Pan J. , Ekert A. . Security analysis of quantum key distribution with small block length and its application to quantum space communications. Phys. Rev. Lett., 2021, 126( 10): 100501 https://doi.org/10.1103/PhysRevLett.126.100501
15	C. Kwek L. , Cao L. , Luo W. , X. Wang Y. , H. Sun S. , B. Wang X. , Q. Liu A. . Chip-based quantum key distribution. AAPPS Bull., 2021, 31( 1): 15 https://doi.org/10.1007/s43673-021-00017-0
16	Y. Gao C. , L. Guo P. , C. Ren B. . Efficient quantum secure direct communication with complete Bell state measurement. Quantum Eng., 2021, 3( 4): e83 https://doi.org/10.1002/que2.83
17	Z. Tang G. , Y. Li C. , Wang M. . Polarization discriminated time-bin phase-encoding measurement device-independent quantum key distribution. Quantum Eng., 2021, 3( 4): e79 https://doi.org/10.1002/que2.79
18	Yan X. , F. Yu Y. , M. Zhang Z. . Entanglement concentration for a non-maximally entangled four-photon cluster state. Front. Phys., 2014, 9 : 640 https://doi.org/10.1007/s11467-014-0435-z
19	Wang H. , C. Ren B. , H. Wang A. , Alsaedi A. , Hayat T. , G. Deng F. . General hyperentanglement concentration for polarization-spatial-time-bin multi-photon systems with linear optics. Front. Phys., 2018, 13 : 130315 https://doi.org/10.1007/s11467-018-0801-3
20	Liu J. , Zhou L. , Zhong W. , B. Sheng Y. . Logic Bell state concentration with parity check measurement. Front. Phys., 2019, 14( 2): 21601 https://doi.org/10.1007/s11467-018-0866-z
21	G. Deng F. , L. Long G. , S. Liu X. . Two-step quantum direct communication protocol using the Einstein−Podolsky−Rosen pair block. Phys. Rev. A, 2003, 68( 4): 042317 https://doi.org/10.1103/PhysRevA.68.042317
22	R. Zhou Z. , B. Sheng Y. , H. Niu P. , G. Yin L. , L. Long G. , Hanzo L. . Measurement-device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron., 2020, 63( 3): 230362 https://doi.org/10.1007/s11433-019-1450-8
23	L. Long G. , Zhang H. . Drastic increase of channel capacity in quantum secure direct communication using masking. Sci. Bull. (Beijing), 2021, 66( 13): 1267 https://doi.org/10.1016/j.scib.2021.04.016
24	B. Sheng Y. , Zhou L. , L. Long G. . One-step quantum secure direct communication. Sci. Bull. (Beijing), 2022, 67( 4): 367 https://doi.org/10.1016/j.scib.2021.11.002
25	Zhou L. , B. Sheng Y. . One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron., 2022, 65( 5): 250311 https://doi.org/10.1007/s11433-021-1863-9
26	Wang C. . Quantum secure direct communication: Intersection of communication and cryptography. Funda. Res., 2021, 1( 1): 91 https://doi.org/10.1016/j.fmre.2021.01.002
27	D. Ye Z. , Pan D. , Sun Z. , G. Du C. , G. Yin L. , L. Long G. . Generic security analysis framework for quantum secure direct communication. Front. Phys., 2021, 16 : 21503 https://doi.org/10.1007/s11467-020-1025-x
28	Lütkenhaus N. , Calsamiglia J. , A. Suominen K. . Bell measurements for teleportation. Phys. Rev. A, 1999, 59( 5): 3295 https://doi.org/10.1103/PhysRevA.59.3295
29	Vaidman L. , Yoran N. . Methods for reliable teleportation. Phys. Rev. A, 1999, 59( 1): 116 https://doi.org/10.1103/PhysRevA.59.116
30	A. Nielsen M. , Knill E. , Laflamme R. . Complete quantum teleportation using nuclear magnetic resonance. Nature, 1998, 396( 6706): 52 https://doi.org/10.1038/23891
31	D. Barrett M. , Chiaverini J. , Schaetz T. , Britton J. , M. Itano W. , D. Jost J. , Knill E. , Langer C. , Leibfried D. , Ozeri R. , J. Wineland D. . Deterministic quantum teleportation of atomic qubits. Nature, 2004, 429( 6993): 737 https://doi.org/10.1038/nature02608
32	Ye L. , C. Guo G. . Scheme for teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A, 2004, 70( 5): 054303 https://doi.org/10.1103/PhysRevA.70.054303
33	P. Williams B. , J. Sadlier R. , S. Humble T. . Superdense coding over optical fiber links with complete Bell-state measurements. Phys. Rev. Lett., 2017, 118( 5): 050501 https://doi.org/10.1103/PhysRevLett.118.050501
34	G. Kwiat P. , Weinfurter H. . Embedded Bell-state analysis. Phys. Rev. A, 1998, 58( 4): R2623 https://doi.org/10.1103/PhysRevA.58.R2623
35	Vallone G. , Ceccarelli R. , De Martini F. , Mataloni P. . Hyperentanglement of two photons in three degrees of freedom. Phys. Rev. A, 2009, 79( 3): 030301 https://doi.org/10.1103/PhysRevA.79.030301
36	L. Wang X. , H. Luo Y. , L. Huang H. , C. Chen M. , E. Su Z. , Liu C. , Chen C. , Li W. , Q. Fang Y. , Jiang X. , Zhang J. , Li L. , L. Liu N. , Y. Lu C. , W. Pan J. . 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett., 2018, 120( 26): 260502 https://doi.org/10.1103/PhysRevLett.120.260502
37	Pile D. . How many bits can a photon carry. Nat. Photonics, 2012, 6( 1): 14 https://doi.org/10.1038/nphoton.2011.330
38	Flamini F. , Spagnolo N. , Sciarrino F. . Photonic quantum information processing: A review. Rep. Prog. Phys., 2019, 82( 1): 016001 https://doi.org/10.1088/1361-6633/aad5b2
39	Y. Wang G. , Ai Q. , C. Ren B. , Li T. , G. Deng F. . Error-detected generation and complete analysis of hyperentangled Bell states for photons assisted by quantum-dot spins in double-sided optical microcavities. Opt. Express, 2016, 24( 25): 28444 https://doi.org/10.1364/OE.24.028444
40	G. Deng F. , C. Ren B. , H. Li X. . Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. (Beijing), 2017, 62( 1): 46 https://doi.org/10.1016/j.scib.2016.11.007
41	C. Wei T. , T. Barreiro J. , G. Kwiat P. . Hyperentangled Bell-state analysis. Phys. Rev. A, 2007, 75 : 060305(R) https://doi.org/10.1103/PhysRevA.75.060305
42	Pisenti N. , P. E. Gaebler C. , W. Lynn T. . Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement. Phys. Rev. A, 2011, 84( 2): 022340 https://doi.org/10.1103/PhysRevA.84.022340
43	H. Li X. , Ghose S. . Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement. Phys. Rev. A, 2017, 96 : 020303(R) https://doi.org/10.1103/PhysRevA.96.020303
44	Y. Gao C. , C. Ren B. , X. Zhang Y. , Ai Q. , G. Deng F. . The linear optical unambiguous discrimination of hyperentangled Bell states assisted by time bin. Ann. Phys., 2019, 531( 10): 1900201 https://doi.org/10.1002/andp.201900201
45	Y. Gao C. , C. Ren B. , X. Zhang Y. , Ai Q. , G. Deng F. . Universal linear-optical hyperentangled Bell-state measurement. Appl. Phys. Express, 2020, 13 : 027004
46	B. Sheng Y. , G. Deng F. , L. Long G. . Complete hyperentangled-Bell-state analysis for quantum communication. Phys. Rev. A, 2010, 82( 3): 032318 https://doi.org/10.1103/PhysRevA.82.032318
47	B. Sheng Y. , Zhou L. . Two-step complete polarization logic Bell-state analysis. Sci. Rep., 2015, 5( 1): 13453 https://doi.org/10.1038/srep13453
48	H. Li X. , Ghose S. . Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity. Phys. Rev. A, 2016, 93( 2): 022302 https://doi.org/10.1103/PhysRevA.93.022302
49	R. Zhang H. , Wang P. , Q. Yu C. , C. Ren B. . Deterministic nondestructive state analysis for polarization spatial-time-bin hyperentanglement with cross-Kerr nonlinearity. Chin. Phys. B, 2021, 30( 3): 030304 https://doi.org/10.1088/1674-1056/abd7d5
50	C. Ren B. , R. Wei H. , Hua M. , Li T. , G. Deng F. . Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities. Opt. Express, 2012, 20( 22): 24664 https://doi.org/10.1364/OE.20.024664
51	J. Wang T. , Lu Y. , L. Long G. . Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities. Phys. Rev. A, 2012, 86( 4): 042337 https://doi.org/10.1103/PhysRevA.86.042337
52	Liu Q. , Zhang M. . Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators. Phys. Rev. A, 2015, 91( 6): 062321 https://doi.org/10.1103/PhysRevA.91.062321
53	Sabag E. , Bouscher S. , Marjieh R. , Hayat A. . Photonic Bell-state analysis based on semiconductor superconductor structures. Phys. Rev. B, 2017, 95( 9): 094503 https://doi.org/10.1103/PhysRevB.95.094503
54	Y. Zheng Y. , X. Liang L. , Zhang M. . Error-heralded generation and self-assisted complete analysis of two photon hyperentangled Bell states through single-sided quantum-dot-cavity systems. Sci. China Phys. Mech. Astron., 2019, 62( 7): 970312 https://doi.org/10.1007/s11433-018-9338-8
55	Cao C. , Zhang L. , H. Han Y. , P. Yin P. , Fan L. , W. Duan Y. , Zhang R. . Complete and faithful hyperentangled-Bell-state analysis of photon systems using a failure-heralded and fidelity-robust quantum gate. Opt. Express, 2020, 28( 3): 2857 https://doi.org/10.1364/OE.384360
56	Y. Wang G. , C. Ren B. , G. Deng F. , L. Long G. . Complete analysis of hyperentangled Bell states assisted with auxiliary hyperentanglement. Opt. Express, 2019, 27( 6): 8994 https://doi.org/10.1364/OE.27.008994
57	Zeng Z. , D. Zhu K. . Complete hyperentangled Bell state analysis assisted by hyperentanglement. Laser Phys. Lett., 2020, 17( 7): 075203 https://doi.org/10.1088/1612-202X/ab9117
58	Li T. , Y. Wang G. , G. Deng F. , L. Long G. . Deterministic error correction for nonlocal spatial-polarization hyperentanglement. Sci. Rep., 2016, 6( 1): 20677 https://doi.org/10.1038/srep20677
59	G. Kwiat P. , Waks E. , G. White A. , Appelbaum I. , H. Eberhard P. . Ultrabright source of polarizationentangled photons. Phys. Rev. A, 1999, 60( 2): R773 https://doi.org/10.1103/PhysRevA.60.R773
60	Ceccarelli R. , Vallone G. , De Martini F. , Mataloni P. , Cabello A. . Experimental entanglement and nonlocality of a two-photon six-qubit cluster state. Phys. Rev. Lett., 2009, 103( 16): 160401 https://doi.org/10.1103/PhysRevLett.103.160401
61	Yabushita A. , Kobayashi T. . Spectroscopy by frequency-entangled photon pairs. Phys. Rev. A, 2004, 69( 1): 013806 https://doi.org/10.1103/PhysRevA.69.013806
62	Yabushita A. , Kobayashi T. . Generation of frequency tunable polarization entangled photon pairs. J. Appl. Phys., 2006, 99( 6): 063101 https://doi.org/10.1063/1.2183355
63	Shu C. , X. Guo X. , Chen P. , M. T. Loy M. , W. Du S. . Narrowband biphotons with polarization-frequencycoupled entanglement. Phys. Rev. A, 2015, 91( 4): 043820 https://doi.org/10.1103/PhysRevA.91.043820
64	Ueno W. , Kaneda F. , Suzuki H. , Nagano S. , Syouji A. , Shimizu R. , Suizu K. , Edamatsu K. . Entangled photon generation in two-period quasi-phase-matched parametric down-conversion. Opt. Express, 2012, 20( 5): 5508 https://doi.org/10.1364/OE.20.005508
65	Kaneda F. , Suzuki H. , Shimizu R. , Edamatsu K. . Direct generation of frequency-bin entangled photons via two-period quasi-phase-matched parametric downconversion. Opt. Express, 2019, 27( 2): 1416 https://doi.org/10.1364/OE.27.001416
66	V. Burlakov A. , P. Kulik S. , O. Rytikov G. , V. Chekhova M. . Biphoton light generation in polarization frequency Bell states. J. Exp. Theor. Phys., 2002, 95( 4): 639 https://doi.org/10.1134/1.1520596
67	H. Huntington E. , C. Ralph T. . Components for optical qubits encoded in sideband modes. Phys. Rev. A, 2004, 69( 4): 042318 https://doi.org/10.1103/PhysRevA.69.042318
68	Bloch M. , W. McLaughlin S. , M. Merolla J. , Patois F. . Frequency-coded quantum key distribution. Opt. Lett., 2007, 32( 3): 301 https://doi.org/10.1364/OL.32.000301
69	Zhang T. , Q. Yin Z. , F. Han Z. , C. Guo G. . A frequency-coded quantum key distribution scheme. Opt. Commun., 2008, 281( 18): 4800 https://doi.org/10.1016/j.optcom.2008.06.009
70	Langrock C. , Diamanti E. , V. Roussev R. , Yamamoto Y. , M. Fejer M. , Takesue H. . Highly efficient singlephoton detection at communication wavelengths by use of upconversion in reverse-proton-exchanged periodically poled LiNbO3 waveguides. Opt. Lett., 2005, 30( 13): 1725 https://doi.org/10.1364/OL.30.001725
71	Takesue H. . Erasing distinguishability using quantum frequency up-conversion. Phys. Rev. Lett., 2008, 101( 17): 173901 https://doi.org/10.1103/PhysRevLett.101.173901
72	Ikuta R. , Kusaka Y. , Kitano T. , Kato H. , Yamamoto T. , Koashi M. , Imoto N. . Wide-band quantum interface for visible-to-telecommunication wavelength conversion. Nat. Commun., 2011, 2( 1): 537 https://doi.org/10.1038/ncomms1544
73	M. Merolla J. , Duraffourg L. , P. Goedgebuer J. , Soujaeff A. , Patois F. , T. Rhodes W. . Integrated quantum key distribution system using single sideband detection. Eur. Phys. J. D, 2002, 18( 2): 141 https://doi.org/10.1140/epjd/e20020017

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