Abstract
We incorporate active and passive quantum error-correcting techniques to protect a set of optical information modes of a continuous-variable quantum information system. Our method uses ancilla modes, entangled modes, and gauge modes (modes in a mixed state) to help correct errors on a set of information modes. A linear-optical encoding circuit consisting of offline squeezers, passive optical devices, feedforward control, conditional modulation, and homodyne measurements performs the encoding. The result is that we extend the entanglement-assisted operator stabilizer formalism for discrete variables to continuous-variable quantum information processing.
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Aly, S.A., Klappenecker, A.: Subsystem code constructions. In: Proceedings of the IEEE International Symposium on Information Theory (arXiv:0712.4321), pp. 369–373 (2008)
Ban M.: Quantum dense coding via a two-mode squeezed-vacuum state. J. Opt. B: Quantum Semiclass. Opt. 1, L1–L9 (1999)
Barnes, R.: Stabilizer codes for continuous-variable quantum error correction. arXiv:quant-ph/0405064 (2004)
Bény, C., Kempf, A., Kribs, D.W.: Quantum error correction on infinite-dimensional hilbert spaces. arXiv:0811.0421 (2008)
Braunstein S.L.: Error correction for continuous quantum variables. Phys. Rev. Let. 80(18), 4084 (1998)
Braunstein S.L.: Quantum error correction for communication with linear optics. Nature 394, 47–49 (1998)
Braunstein S.L.: Squeezing as an irreducible resource. Phys. Rev. A 71(5), 055801 (2005)
Braunstein S.L., Kimble H.J.: Teleportation of continuous quantum variables. Phys. Rev. Let. 80, 869–872 (1998)
Braunstein S.L., Kimble H.J.: Dense coding for continuous variables. Phys. Rev. A 61, 042, 302 (2000)
Braunstein S.L., van Loock P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005)
Braunstein, S.L., Pati, A. (eds.): Quantum Information with Continuous Variables. Springer (2003)
Brun, T., Devetak, I., Hsieh, M.H.: General entanglement-assisted quantum error-correcting codes. In: IEEE International Symposium on Information Theory, pp. 2101–2105 (2007)
Brun, T.A., Devetak, I., Hsieh, M.H.: Catalytic quantum error correction. arXiv:quant-ph/0608027 (2006)
Brun T.A., Devetak I., Hsieh M.H.: Correcting quantum errors with entanglement. Science 314(5798), 436–439 (2006)
Calderbank A., Rains E., Shor P., Sloane N.: Quantum error correction via codes over gf(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)
Calderbank A.R., Rains E.M., Shor P.W., Sloane N.J.A.: Quantum error correction and orthogonal geometry. Phys. Rev. Let. 78(3), 405–408 (1997). doi:10.1103/PhysRevLett.78.405
Calderbank A.R., Shor P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098–1105 (1996). doi:10.1103/PhysRevA.54.1098
Filip R., Marek P., Andersen U.L.: Measurement-induced continuous-variable quantum interactions. Phys. Rev. A 71(4), 042308 (2005)
Furusawa A., Srensen J.L., Braunstein S.L., Fuchs C.A., Kimble H.J., Polzik E.S.: Unconditional quantum teleportation. Science 282(5389), 706–709 (1998)
Gottesman, D.: Stabilizer codes and quantum error correction. Ph.D. thesis, California Institue of Technology (1997)
Gottesman D., Kitaev A., Preskill J.: Encoding a qubit in an oscillator. Phys. Rev. A 64(1), 012, 310 (2001). doi:10.1103/PhysRevA.64.012310
Hsieh M.H., Devetak I., Brun T.: General entanglement-assisted quantum error-correcting codes. Phys. Rev. A 76(6), 062313 (2007). doi:10.1103/PhysRevA.76.062313
Knill E., Laflamme R., Viola L.: Theory of quantum error correction for general noise. Phys. Rev. Let. 84(11), 2525–2528 (2000). doi:10.1103/PhysRevLett.84.2525
Kribs D., Laflamme R., Poulin D.: Unified and generalized approach to quantum error correction. Phys. Rev. Let. 94(18), 180501 (2005). doi:10.1103/PhysRevLett.94.180501
Kribs D.W., Laflamme R., Poulin D., Lesosky M.: Operator quantum error correction. Quant. Inf. Comp. 6, 383–399 (2006)
Kribs D.W., Spekkens R.W.: Quantum error-correcting subsystems are unitarily recoverable subsystems. Phys. Rev. A 74(4), 042329 (2006). doi:10.1103/PhysRevA.74.042329
Li X., Pan Q., Jing J., Zhang J., Xie C., Peng K.: Quantum dense coding exploiting a bright einstein-podolsky-rosen beam. Phys. Rev. Let. 88(4), 047, 904 (2002). doi:10.1103/PhysRevLett.88.047904
Lidar D.A., Chuang I.L., Whaley K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Let. 81(12), 2594–2597 (1998). doi:10.1103/PhysRevLett.81.2594
Lloyd S., Slotine J.J.E.: Analog quantum error correction. Phys. Rev. Let. 80(18), 4088–4091 (1998). doi:10.1103/PhysRevLett.80.4088
Mizuno J., Wakui K., Furusawa A., Sasaki M.: Experimental demonstration of entanglement-assisted coding using a two-mode squeezed vacuum state. Phys. Rev. A 71(1), 012304 (2005)
Nielsen M.A., Poulin D.: Algebraic and information-theoretic conditions for operator quantum error correction. Phys. Rev. A 75(6), 064304 (2007). doi:10.1103/PhysRevA.75.064304
Niset J., Andersen U.L., Cerf N.J.: Experimentally feasible quantum erasure-correcting code for continuous variables. Phys. Rev. Let. 101(13), 130503 (2008). doi:10.1103/PhysRevLett.101.130503
Poulin D.: Stabilizer formalism for operator quantum error correction. Phys. Rev. Let. 95(23), 230504 (2005). doi:10.1103/PhysRevLett.95.230504
Shor P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), R2493–R2496 (1995). doi:10.1103/PhysRevA.52.R2493
Steane A.M.: Error correcting codes in quantum theory. Phys. Rev. Let. 77(5), 793–797 (1996). doi:10.1103/PhysRevLett.77.793
Vaidman L.: Teleportation of quantum states. Phys. Rev. A 49(2), 1473–1476 (1994). doi:10.1103/PhysRevA.49.1473
Wilde, M.M., Brun, T.A.: Entanglement-assisted quantum convolutional coding. arXiv:0712.2223 (2007)
Wilde M.M., Brun T.A.: Optimal entanglement formulas for entanglement-assisted quantum coding. Phys. Rev. A 77, 064,302 (2008)
Wilde M.M., Brun T.A., Dowling J.P., Lee H.: Coherent communication with linear optics. Phys. Rev. A 77, 022,321 (2007)
Wilde M.M., Krovi H., Brun T.A.: Coherent communication with continuous quantum variables. Phys. Rev. A 75(6), 060303 (2007). doi:10.1103/PhysRevA.75.060303
Wilde, M.M., Krovi, H., Brun, T.A.: Convolutional entanglement distillation. arXiv:0708.3699 (2007)
Wilde M.M., Krovi H., Brun T.A.: Entanglement-assisted quantum error correction with linear optics. Phys. Rev. A 76, 052,308 (2007)
Yoshikawa J.I., Hayashi T., Akiyama T., Takei N., Huck A., Andersen U.L., Furusawa A.: Demonstration of deterministic and high fidelity squeezing of quantum information. Phys. Rev. A 76(6), 060301 (2007). doi:10.1103/PhysRevA.76.060301
Yoshikawa J.I., Miwa Y., Huck A., Andersen U.L., van Loock P., Furusawa A.: Demonstration of a quantum nondemolition sum gate. Phys. Rev. Let. 101(25), 250501 (2008). doi:10.1103/PhysRevLett.101.250501
Zanardi P., Rasetti M.: Error avoiding quantum codes. Mod. Phys. Lett. B 11, 1085–1093 (1997)
Zanardi P., Rasetti M.: Noiseless quantum codes. Phys. Rev. Let. 79(17), 3306–3309 (1997). doi:10.1103/PhysRevLett.79.3306
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Wilde, M.M., Brun, T.A. Protecting quantum information with entanglement and noisy optical modes. Quantum Inf Process 8, 401–413 (2009). https://doi.org/10.1007/s11128-009-0117-x
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DOI: https://doi.org/10.1007/s11128-009-0117-x
Keywords
- Operator quantum error correction
- Stabilizer formalism
- Entanglement-assisted quantum error correction
- Continuous variables
- Linear-optical quantum computation