Abstract

Channel noise is the main issue which reduces the efficiency of quantum communication. Here we present an efficient scheme for quantum key distribution against collective-rotation channel noise using polarization and transverse spatial mode of photons. Exploiting the two single-photon Bell states and two-photon hyperentangled Bell states in the polarization and the transverse spatial mode degrees of freedom (DOFs), the mutually unbiased bases can be encoded for logical qubits against the collective-rotation noise. Our scheme shows noiseless subspaces can be made up of two DOFs of two photons instead of multiple photons, which will reduce the resources required for noiseless subspaces and depress the photonic loss sensitivity. Moreover, the two single-photon Bell states and two-photon hyperentangled Bell states are symmetrical to the two photons, which means the relative order of the two photons is not required in our scheme, so the receiver only needs to measure the state of each photon, which makes our protocol easy to execute in experiment than the previous works.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

S.-S. Chen, L. Zhou, W. Zhong, and Y.-B. Sheng, “Three-step three-party quantum secure direct communication,” Sci. China: Phys., Mech. Astron. 61(9), 90312 (2018).
[Crossref]

Y.-B. Sheng and L. Zhou, “Blind quantum computation with a noise channel,” Phys. Rev. A 98(5), 052343 (2018).
[Crossref]

M. Wang, J. Xu, F. Yan, and T. Gao, “Entanglement concentration for polarization–spatial–time-bin hyperentangled bell states,” EPL 123(6), 60002 (2018).
[Crossref]

M. H. M. Passos, W. F. Balthazar, A. Z. Khoury, M. Hor-Meyll, L. Davidovich, and J. A. O. Huguenin, “Experimental investigation of environment-induced entanglement using an all-optical setup,” Phys. Rev. A 97(2), 022321 (2018).
[Crossref]

2017 (3)

2016 (4)

J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, “Experimental quantum secure direct communication with single photons,” Light: Sci. Appl. 5(9), e16144 (2016).
[Crossref]

M. Wang, F. Yan, and T. Gao, “Generation of four-photon polarization entangled decoherence-free states with cross-kerr nonlinearity,” Sci. Rep. 6(1), 38233 (2016).
[Crossref]

L. Zhou and Y.-B. Sheng, “Purification of logic-qubit entanglement,” Sci. Rep. 6(1), 28813 (2016).
[Crossref]

W. F. Balthazar, C. E. R. Souza, D. P. Caetano, E. F. Galvão, J. A. O. Huguenin, and A. Z. Khoury, “Tripartite nonseparability in classical optics,” Opt. Lett. 41(24), 5797–5800 (2016).
[Crossref]

2015 (2)

X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17(3), 033033 (2015).
[Crossref]

2014 (2)

C. Wang, T.-J. Wang, Y. Zhang, R.-Z. Jiao, and G.-S. Jin, “Concentration of entangled nitrogen-vacancy centers in decoherence free subspace,” Opt. Express 22(2), 1551–1559 (2014).
[Crossref]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113(6), 060503 (2014).
[Crossref]

2013 (1)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88(3), 032305 (2013).
[Crossref]

2012 (2)

Y.-B. Sheng, L. Zhou, S.-M. Zhao, and B.-Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85(1), 012307 (2012).
[Crossref]

V. D’ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3(1), 961 (2012).
[Crossref]

2011 (4)

2010 (3)

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82(3), 033833 (2010).
[Crossref]

Y.-B. Sheng, F.-G. Deng, and G. L. Long, “Complete hyperentangled-bell-state analysis for quantum communication,” Phys. Rev. A 82(3), 032318 (2010).
[Crossref]

X. Yin, Y. Liu, Z. Zhang, W. Zhang, and Z. Zhang, “Perfect teleportation of an arbitrary three-qubit state with the highly entangled six-qubit genuine state,” Sci. China: Phys., Mech. Astron. 53(11), 2059–2063 (2010).
[Crossref]

2009 (1)

X.-M. Xiu, L. Dong, Y.-J. Gao, and F. Chi, “Quantum key distribution protocols with six-photon states against collective noise,” Opt. Commun. 282(20), 4171–4174 (2009).
[Crossref]

2008 (2)

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

C. Souza, C. Borges, A. Khoury, J. Huguenin, L. Aolita, and S. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[Crossref]

2007 (3)

L. Aolita and S. Walborn, “Quantum communication without alignment using multiple-qubit single-photon states,” Phys. Rev. Lett. 98(10), 100501 (2007).
[Crossref]

T. Yamamoto, R. Nagase, J. Shimamura, Ş. K. Özdemir, M. Koashi, and N. Imoto, “Experimental ancilla-assisted qubit transmission against correlated noise using quantum parity checking,” New J. Phys. 9(6), 191 (2007).
[Crossref]

X.-H. Li, F.-G. Deng, and H.-Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91(14), 144101 (2007).
[Crossref]

2006 (2)

F. Gao, F.-Z. Guo, Q.-Y. Wen, and F.-C. Zhu, “Quantum key distribution without alternative measurements and rotations,” Phys. Lett. A 349(1-4), 53–58 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation,” Appl. Phys. Lett. 88(22), 221102 (2006).
[Crossref]

2005 (8)

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72(1), 012326 (2005).
[Crossref]

Z.-J. Zhang, Z.-X. Man, and S.-H. Shi, “An efficient multiparty quantum key distribution scheme,” Int. J. Quantum Inf. 03(03), 555–560 (2005).
[Crossref]

D. Kalamidas, “Single-photon quantum error rejection and correction with linear optics,” Phys. Lett. A 343(5), 331–335 (2005).
[Crossref]

T. Yamamoto, J. Shimamura, Ş. Özdemir, M. Koashi, and N. Imoto, “Faithful qubit distribution assisted by one additional qubit against collective noise,” Phys. Rev. Lett. 95(4), 040503 (2005).
[Crossref]

F.-L. Yan and T. Gao, “Quantum secret sharing between multiparty and multiparty without entanglement,” Phys. Rev. A 72(1), 012304 (2005).
[Crossref]

C. Wang, F.-G. Deng, Y.-S. Li, X.-S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A 71(4), 044305 (2005).
[Crossref]

T. Yamamoto, J. Shimamura, Ş. Özdemir, M. Koashi, and N. Imoto, “Faithful qubit distribution assisted by one additional qubit against collective noise,” Phys. Rev. Lett. 95(4), 040503 (2005).
[Crossref]

J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, “Generation of hyperentangled photon pairs,” Phys. Rev. Lett. 95(26), 260501 (2005).
[Crossref]

2004 (6)

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J.-C. Boileau, D. Gottesman, R. Laflamme, D. Poulin, and R. Spekkens, “Robust polarization-based quantum key distribution over a collective-noise channel,” Phys. Rev. Lett. 92(1), 017901 (2004).
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J.-C. Boileau, R. Laflamme, M. Laforest, and C. Myers, “Robust quantum communication using a polarization-entangled photon pair,” Phys. Rev. Lett. 93(22), 220501 (2004).
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F.-G. Deng and G. L. Long, “Secure direct communication with a quantum one-time pad,” Phys. Rev. A 69(5), 052319 (2004).
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Z. Zhang, Z. Man, and Y. Li, “Improving wójcik’s eavesdropping attack on the ping–pong protocol,” Phys. Lett. A 333(1-2), 46–50 (2004).
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2003 (4)

Z. D. Walton, A. F. Abouraddy, A. V. Sergienko, B. E. Saleh, and M. C. Teich, “Decoherence-free subspaces in quantum key distribution,” Phys. Rev. Lett. 91(8), 087901 (2003).
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2002 (4)

C. Simon and J.-W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89(25), 257901 (2002).
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2001 (4)

D. Bouwmeester, “Bit-flip-error rejection in optical quantum communication,” Phys. Rev. A 63(4), 040301 (2001).
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J.-W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, “Entanglement purification for quantum communication,” Nature 410(6832), 1067–1070 (2001).
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Z. Zhao, J.-W. Pan, and M. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64(1), 014301 (2001).
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2000 (2)

P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence-free subspaces,” Science 290(5491), 498–501 (2000).
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1999 (2)

H.-K. Lo and H. F. Chau, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283(5410), 2050–2056 (1999).
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1997 (3)

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1996 (3)

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of laguerre–gaussian laser modes,” Am. J. Phys. 64(1), 77–82 (1996).
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1995 (1)

B. Huttner, N. Imoto, N. Gisin, and T. Mor, “Quantum cryptography with coherent states,” Phys. Rev. A 51(3), 1863–1869 (1995).
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1993 (3)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
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M. W. Beijersbergen, L. Allen, H. Van der Veen, and J. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
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P. D. Townsend, J. Rarity, and P. Tapster, “Single photon interference in 10 km long optical fibre interferometer,” Electron. Lett. 29(7), 634–635 (1993).
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1992 (2)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68(21), 3121–3124 (1992).
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C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, “Experimental quantum cryptography,” J. Cryptol. 5(1), 3–28 (1992).
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1991 (1)

A. K. Ekert, “Quantum cryptography based on bell’s theorem,” Phys. Rev. Lett. 67(6), 661–663 (1991).
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1989 (1)

M. Martinelli, “A universal compensator for polarization changes induced by birefringence on a retracing beam,” Opt. Commun. 72(6), 341–344 (1989).
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Figures (4)

Fig. 1.
Fig. 1. (a) The polarization states. The first line presents horizontal and vertical polarizations, and the second line presents left and right circular polarizations. (b) The transverse spatial modes. The first line presents $\rm HG_{10}$ mode and $\rm HG_{01}$ mode, and the second line presents $\rm LG_{\pm 1,0}$ modes.
Fig. 2.
Fig. 2. The detection setup for the logical qubit states with the measurement basis $\{\left |H\right \rangle ,\left |V\right \rangle ,\rm HG\}$. The detection device includes Mach-Zehnder interferometer with an additional mirror (MZIM) and polarizing beam splitters (PBSs), where the MZIM is composed by two 50:50 beam splitters (BSs) and three high-reflectivity mirrors. The polarizing beam splitter (PBS) is used to transmit the polarization state $\left |H\right \rangle$ and reflect the polarization state $\left |V\right \rangle$.
Fig. 3.
Fig. 3. The detection setup for the logical qubit states with the measurement basis $\{\left |L\right \rangle ,\left |R\right \rangle ,\rm LG\}$, including the q-plate (q=1/2), a Mach-Zehnder interferometer with a Dove prism$@45{^\circ }$, and circular-polarization analysis setup. The Mach-Zehnder interferometer with a Dove prism@$45{^\circ }$ is composed by two 50:50 BSs, a Dove prism@45° and two reflective mirrors, and the circular-polarization analysis setup is composed by quarter-wave plate, half-wave plate, and PBS. Dove$@45{^\circ }$ represents the Dove prism aligned at $45{^\circ }$, which can rotate the beam by $\alpha =90{^\circ }$. $\frac {\lambda }{4}$ represents quarter-wave plate aligned at $90{^\circ }$, and $\frac {\lambda }{2}$ represents half-wave plate aligned at $-22.5{^\circ }$.
Fig. 4.
Fig. 4. Key rate versus the maximal secure transmission distance L with different protocols. Blue Solid line: QKD protocol using weak coherent source. Red Dash line: modified QKD protocol with logical basis.

Tables (3)

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Table 1. The decoding results of logical qubit states with measurement basis { | H , | V , H G }.

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Table 2. The error rates for the different ways of eavesdropping attack.

Tables Icon

Table 3. The list of experimental parameters used in the simulations

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

| Ψ 0 = 1 2 ( | H | h + | V | v ) 1 ( | H | h + | V | v ) 2 = a + b ,
| Ψ 1 = 1 2 ( | H | v | V | h ) 1 ( | H | v | V | h ) 2 = c d ,
| Φ 0 = 1 2 ( | H | H + | V | V ) 12 ( | h | h + | v | v ) 12 = a + c ,
| Φ 1 = 1 2 ( | H | V | V | H ) 12 ( | h | v | v | h ) 12 = b d ,
a = 1 2 [ ( | H | h ) 1 ( | H | h ) 2 + ( | V | v ) 1 ( | V | v ) 2 ] ,
b = 1 2 [ ( | H | h ) 1 ( | V | v ) 2 + ( | V | v ) 1 ( | H | h ) 2 ] ,
c = 1 2 [ ( | H | v ) 1 ( | H | v ) 2 + ( | V | h ) 1 ( | V | h ) 2 ] ,
d = 1 2 [ ( | H | v ) 1 ( | V | h ) 2 + ( | V | h ) 1 ( | H | v ) 2 ] .
| Ψ 0 = 1 2 ( | R | l + | L | r ) 1 ( | R | l + | L | r ) 2 = e + f ,
| Ψ 1 = 1 2 ( | R | l | L | r ) 1 ( | R | l | L | r ) 2 = e f ,
| Φ 0 = 1 2 ( | R | L + | L | R ) 12 ( | r | l + | l | r ) 12 = e + g ,
| Φ 1 = 1 2 ( | R | L | L | R ) 12 ( | r | l | l | r ) 12 = e g ,
e = 1 2 [ ( | R | l ) 1 ( | L | r ) 2 + ( | L | r ) 1 ( | R | l ) 2 ] ,
f = 1 2 [ ( | R | l ) 1 ( | R | l ) 2 + ( | L | r ) 1 ( | L | r ) 2 ] ,
g = 1 2 [ ( | R | r ) 1 ( | L | l ) 2 + ( | L | l ) 1 ( | R | r ) 2 ] .
Y 1 Z = μ μ ν ν 2 ( Q v e v Q μ e μ v 2 μ 2 μ 2 v 2 μ 2 Y 0 ) ,
e 1 X = e 0 Y 0 + e d η B η q Y 1 2 ,
R = q { Q μ f ( E μ ) H 2 ( E μ ) + Q 1 [ 1 H 2 ( e 1 ) ] } .

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