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

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.

Graphical abstract

Keywords

hyperentangled Bell states analysis / multiple degrees of freedom / time interval

References

[1] M. A. Nielsen I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000

[2] R. Raussendorf , H. J. Briegel . A one-way quantum computer. Phys. Rev. Lett., 2001, 86( 22): 5188

[3] R. Raussendorf , D. E. Browne , H. J. Briegel . Measurement-based quantum computation on cluster states. Phys. Rev. A, 2003, 68( 2): 022312

[4] S. Liu , Y. Lou , J. Jing . Orbital angular momentum multiplexed deterministic all-optical quantum teleportation. Nat. Commun., 2020, 11( 1): 3875

[5] S. Langenfeld , S. Welte , L. Hartung , S. Daiss , P. Thomas , O. Morin , E. Distante , G. Rempe . Quantum teleportation between remote qubit memories with only a single photon as a resource. Phys. Rev. Lett., 2021, 126( 13): 130502

[6] W. Ning , X. J. Huang , P. R. Han , H. Li , H. Deng , Z. B. Yang , Y. Xia , K. Xu , D. N. Zheng , S. B. Zheng . Deterministic entanglement swapping in a superconducting circuit. Phys. Rev. Lett., 2019, 123( 6): 060502

[7] Z. X. Ji , P. R. Fan , H. G. Zhang . Entanglement swapping for Bell states and Greenberger−Horne− Zeilinger states in qubit systems. Physica A, 2022, 585 : 126400

[8] C. H. Bennett , S. J. Wiesner . Communication via one- and two-particle operators on Einstein−Podolsky−Rosen states. Phys. Rev. Lett., 1992, 69( 20): 2881

[9] Y. Guo , B. H. Liu , C. F. Li , G. C. Guo . Advances in quantum dense coding. Adv. Quantum Technol., 2019, 2( 5−6): 1900011

[10] P. Wang , C. Q. Yu , Z. X. Wang , R. Y. Yuan , F. F. Du , B. C. Ren . Hyperentanglement-assisted hyperdistillation for hyper-encoding photon system. Front. Phys., 2022, 17 : 31501

[11] G. L. Long , X. S. Liu . Theoretically efficient highcapacity quantum-key-distribution scheme. Phys. Rev. A, 2002, 65( 3): 032302

[12] X. H. Li , F. G. Deng , H. Y. Zhou . Efficient quantum key distribution over a collective noise channel. Phys. Rev. A, 2008, 78( 2): 022321

[13] L. M. Liang , S. H. Sun , M. S. Jiang , C. Y. Li . Security analysis on some experimental quantum key distribution systems with imperfect optical and electrical devices. Front. Phys., 2014, 9 : 613

[14] C. C. W. Lim , F. Xu , J. W. Pan , A. Ekert . Security analysis of quantum key distribution with small block length and its application to quantum space communications. Phys. Rev. Lett., 2021, 126( 10): 100501

[15] L. C. Kwek , L. Cao , W. Luo , Y. X. Wang , S. H. Sun , X. B. Wang , A. Q. Liu . Chip-based quantum key distribution. AAPPS Bull., 2021, 31( 1): 15

[16] C. Y. Gao , P. L. Guo , B. C. Ren . Efficient quantum secure direct communication with complete Bell state measurement. Quantum Eng., 2021, 3( 4): e83

[17] G. Z. Tang , C. Y. Li , M. Wang . Polarization discriminated time-bin phase-encoding measurement device-independent quantum key distribution. Quantum Eng., 2021, 3( 4): e79

[18] X. Yan , Y. F. Yu , Z. M. Zhang . Entanglement concentration for a non-maximally entangled four-photon cluster state. Front. Phys., 2014, 9 : 640

[19] H. Wang , B. C. Ren , A. H. Wang , A. Alsaedi , T. Hayat , F. G. Deng . General hyperentanglement concentration for polarization-spatial-time-bin multi-photon systems with linear optics. Front. Phys., 2018, 13 : 130315

[20] J. Liu , L. Zhou , W. Zhong , Y. B. Sheng . Logic Bell state concentration with parity check measurement. Front. Phys., 2019, 14( 2): 21601

[21] F. G. Deng , G. L. Long , X. S. Liu . Two-step quantum direct communication protocol using the Einstein−Podolsky−Rosen pair block. Phys. Rev. A, 2003, 68( 4): 042317

[22] Z. R. Zhou , Y. B. Sheng , P. H. Niu , L. G. Yin , G. L. Long , L. Hanzo . Measurement-device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron., 2020, 63( 3): 230362

[23] G. L. Long , H. Zhang . Drastic increase of channel capacity in quantum secure direct communication using masking. Sci. Bull. (Beijing), 2021, 66( 13): 1267

[24] Y. B. Sheng , L. Zhou , G. L. Long . One-step quantum secure direct communication. Sci. Bull. (Beijing), 2022, 67( 4): 367

[25] L. Zhou , Y. B. Sheng . One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron., 2022, 65( 5): 250311

[26] C. Wang . Quantum secure direct communication: Intersection of communication and cryptography. Funda. Res., 2021, 1( 1): 91

[27] Z. D. Ye , D. Pan , Z. Sun , C. G. Du , L. G. Yin , G. L. Long . Generic security analysis framework for quantum secure direct communication. Front. Phys., 2021, 16 : 21503

[28] N. Lütkenhaus , J. Calsamiglia , K. A. Suominen . Bell measurements for teleportation. Phys. Rev. A, 1999, 59( 5): 3295

[29] L. Vaidman , N. Yoran . Methods for reliable teleportation. Phys. Rev. A, 1999, 59( 1): 116

[30] M. A. Nielsen , E. Knill , R. Laflamme . Complete quantum teleportation using nuclear magnetic resonance. Nature, 1998, 396( 6706): 52

[31] M. D. Barrett , J. Chiaverini , T. Schaetz , J. Britton , W. M. Itano , J. D. Jost , E. Knill , C. Langer , D. Leibfried , R. Ozeri , D. J. Wineland . Deterministic quantum teleportation of atomic qubits. Nature, 2004, 429( 6993): 737

[32] L. Ye , G. C. Guo . Scheme for teleportation of an unknown atomic state without the Bell-state measurement. Phys. Rev. A, 2004, 70( 5): 054303

[33] B. P. Williams , R. J. Sadlier , T. S. Humble . Superdense coding over optical fiber links with complete Bell-state measurements. Phys. Rev. Lett., 2017, 118( 5): 050501

[34] P. G. Kwiat , H. Weinfurter . Embedded Bell-state analysis. Phys. Rev. A, 1998, 58( 4): R2623

[35] G. Vallone , R. Ceccarelli , F. De Martini , P. Mataloni . Hyperentanglement of two photons in three degrees of freedom. Phys. Rev. A, 2009, 79( 3): 030301

[36] X. L. Wang , Y. H. Luo , H. L. Huang , M. C. Chen , Z. E. Su , C. Liu , C. Chen , W. Li , Y. Q. Fang , X. Jiang , J. Zhang , L. Li , N. L. Liu , C. Y. Lu , J. W. Pan . 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett., 2018, 120( 26): 260502

[37] D. Pile . How many bits can a photon carry. Nat. Photonics, 2012, 6( 1): 14

[38] F. Flamini , N. Spagnolo , F. Sciarrino . Photonic quantum information processing: A review. Rep. Prog. Phys., 2019, 82( 1): 016001

[39] G. Y. Wang , Q. Ai , B. C. Ren , T. Li , F. G. Deng . 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

[40] F. G. Deng , B. C. Ren , X. H. Li . Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. (Beijing), 2017, 62( 1): 46

[41] T. C. Wei , J. T. Barreiro , P. G. Kwiat . Hyperentangled Bell-state analysis. Phys. Rev. A, 2007, 75 : 060305(R)

[42] N. Pisenti , C. P. E. Gaebler , T. W. Lynn . Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement. Phys. Rev. A, 2011, 84( 2): 022340

[43] X. H. Li , S. Ghose . Hyperentangled Bell-state analysis and hyperdense coding assisted by auxiliary entanglement. Phys. Rev. A, 2017, 96 : 020303(R)

[44] C. Y. Gao , B. C. Ren , Y. X. Zhang , Q. Ai , F. G. Deng . The linear optical unambiguous discrimination of hyperentangled Bell states assisted by time bin. Ann. Phys., 2019, 531( 10): 1900201

[45] C. Y. Gao , B. C. Ren , Y. X. Zhang , Q. Ai , F. G. Deng . Universal linear-optical hyperentangled Bell-state measurement. Appl. Phys. Express, 2020, 13 : 027004

[46] Y. B. Sheng , F. G. Deng , G. L. Long . Complete hyperentangled-Bell-state analysis for quantum communication. Phys. Rev. A, 2010, 82( 3): 032318

[47] Y. B. Sheng , L. Zhou . Two-step complete polarization logic Bell-state analysis. Sci. Rep., 2015, 5( 1): 13453

[48] X. H. Li , S. Ghose . Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity. Phys. Rev. A, 2016, 93( 2): 022302

[49] H. R. Zhang , P. Wang , C. Q. Yu , B. C. Ren . Deterministic nondestructive state analysis for polarization spatial-time-bin hyperentanglement with cross-Kerr nonlinearity. Chin. Phys. B, 2021, 30( 3): 030304

[50] B. C. Ren , H. R. Wei , M. Hua , T. Li , F. G. Deng . Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities. Opt. Express, 2012, 20( 22): 24664

[51] T. J. Wang , Y. Lu , G. L. Long . 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

[52] Q. Liu , M. Zhang . Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators. Phys. Rev. A, 2015, 91( 6): 062321

[53] E. Sabag , S. Bouscher , R. Marjieh , A. Hayat . Photonic Bell-state analysis based on semiconductor superconductor structures. Phys. Rev. B, 2017, 95( 9): 094503

[54] Y. Y. Zheng , L. X. Liang , M. Zhang . 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

[55] C. Cao , L. Zhang , Y. H. Han , P. P. Yin , L. Fan , Y. W. Duan , R. Zhang . 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

[56] G. Y. Wang , B. C. Ren , F. G. Deng , G. L. Long . Complete analysis of hyperentangled Bell states assisted with auxiliary hyperentanglement. Opt. Express, 2019, 27( 6): 8994

[57] Z. Zeng , K. D. Zhu . Complete hyperentangled Bell state analysis assisted by hyperentanglement. Laser Phys. Lett., 2020, 17( 7): 075203

[58] T. Li , G. Y. Wang , F. G. Deng , G. L. Long . Deterministic error correction for nonlocal spatial-polarization hyperentanglement. Sci. Rep., 2016, 6( 1): 20677

[59] P. G. Kwiat , E. Waks , A. G. White , I. Appelbaum , P. H. Eberhard . Ultrabright source of polarizationentangled photons. Phys. Rev. A, 1999, 60( 2): R773

[60] R. Ceccarelli , G. Vallone , F. De Martini , P. Mataloni , A. Cabello . Experimental entanglement and nonlocality of a two-photon six-qubit cluster state. Phys. Rev. Lett., 2009, 103( 16): 160401

[61] A. Yabushita , T. Kobayashi . Spectroscopy by frequency-entangled photon pairs. Phys. Rev. A, 2004, 69( 1): 013806

[62] A. Yabushita , T. Kobayashi . Generation of frequency tunable polarization entangled photon pairs. J. Appl. Phys., 2006, 99( 6): 063101

[63] C. Shu , X. X. Guo , P. Chen , M. M. T. Loy , S. W. Du . Narrowband biphotons with polarization-frequencycoupled entanglement. Phys. Rev. A, 2015, 91( 4): 043820

[64] W. Ueno , F. Kaneda , H. Suzuki , S. Nagano , A. Syouji , R. Shimizu , K. Suizu , K. Edamatsu . Entangled photon generation in two-period quasi-phase-matched parametric down-conversion. Opt. Express, 2012, 20( 5): 5508

[65] F. Kaneda , H. Suzuki , R. Shimizu , K. Edamatsu . Direct generation of frequency-bin entangled photons via two-period quasi-phase-matched parametric downconversion. Opt. Express, 2019, 27( 2): 1416

[66] A. V. Burlakov , S. P. Kulik , G. O. Rytikov , M. V. Chekhova . Biphoton light generation in polarization frequency Bell states. J. Exp. Theor. Phys., 2002, 95( 4): 639

[67] E. H. Huntington , T. C. Ralph . Components for optical qubits encoded in sideband modes. Phys. Rev. A, 2004, 69( 4): 042318

[68] M. Bloch , S. W. McLaughlin , J. M. Merolla , F. Patois . Frequency-coded quantum key distribution. Opt. Lett., 2007, 32( 3): 301

[69] T. Zhang , Z. Q. Yin , Z. F. Han , G. C. Guo . A frequency-coded quantum key distribution scheme. Opt. Commun., 2008, 281( 18): 4800

[70] C. Langrock , E. Diamanti , R. V. Roussev , Y. Yamamoto , M. M. Fejer , H. Takesue . 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

[71] H. Takesue . Erasing distinguishability using quantum frequency up-conversion. Phys. Rev. Lett., 2008, 101( 17): 173901

[72] R. Ikuta , Y. Kusaka , T. Kitano , H. Kato , T. Yamamoto , M. Koashi , N. Imoto . Wide-band quantum interface for visible-to-telecommunication wavelength conversion. Nat. Commun., 2011, 2( 1): 537

[73] J. M. Merolla , L. Duraffourg , J. P. Goedgebuer , A. Soujaeff , F. Patois , W. T. Rhodes . Integrated quantum key distribution system using single sideband detection. Eur. Phys. J. D, 2002, 18( 2): 141

RIGHTS & PERMISSIONS

Higher Education Press