Tight quantum teleportation without a shared reference frame

We present a new scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other proposals, our method requires the same amount of classical communication and entangled resources as conventional teleportation, does not reveal any reference frame information, and is robust against changes in reference frame alignment while the protocol is underway. The mathematical foundation of our scheme is a unitary error basis which is permuted up to a phase by the conjugation action of the group. We completely classify instances of our scheme for qubits, exhibit concrete constructions in higher dimension, and provide a method for proving nonexistence in some cases.

[1]  C. Curtis,et al.  Representation theory of finite groups and associated algebras , 1962 .

[2]  David Paul Kletzing.  Structure and Representations of Q-Groups , 1984 .

[3]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[4]  S. J. van Enk.  The physical meaning of phase and its importance for quantum teleportation , 2001 .

[5]  S. J. van Enk.  The physical meaning of phase and its importance for quantum teleportation , 2001 .

[6]  R. Werner.  All teleportation and dense coding schemes , 2000, quant-ph/0003070.

[7]  H. Bechmann-Pasquinucci,et al.  Quantum cryptography , 2001, quant-ph/0101098.

[8]  Unspeakable quantum information , 2002, quant-ph/0201017.

[9]  F Verstraete,et al.  Quantum nonlocality in the presence of superselection rules and data hiding protocols. , 2003, Physical review letters.

[10]  J. Preskill,et al.  Superselection rules and quantum protocols , 2003, quant-ph/0310088.

[11]  T. Rudolph,et al.  Decoherence-full subsystems and the cryptographic power of a private shared reference frame , 2004, quant-ph/0403161.

[12]  W. Munro,et al.  Low Cost and Compact Quantum Cryptography , 2006, quant-ph/0608213.

[13]  T. Rudolph,et al.  Reference frames, superselection rules, and quantum information , 2006, quant-ph/0610030.

[14]  J.G. Rarity,et al.  Low Cost Quantum Secret Key Growing for Consumer Transactions , 2007, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[15]  R. Spekkens,et al.  The resource theory of quantum reference frames: manipulations and monotones , 2007, 0711.0043.

[16]  C. Souza,et al.  Quantum key distribution without a shared reference frame , 2008 .

[17]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .

[18]  V. Scarani,et al.  Reference-frame-independent quantum key distribution , 2010, 1003.1050.

[19]  Ferenc Szöllősi.  Construction, classification and parametrization of complex Hadamard matrices , 2011 .

[20]  P. Perinotti,et al.  Teleportation transfers only speakable quantum information , 2010, 1008.0967.

[21]  G. Gour,et al.  Alignment of reference frames and an operational interpretation for the G-asymmetry , 2012, 1202.3163.

[22]  V. D'Ambrosio,et al.  Complete experimental toolbox for alignment-free quantum communication , 2012, Nature Communications.

[23]  L. Bacsardi,et al.  On the way to quantum-based satellite communication , 2013, IEEE Communications Magazine.

[24]  Wolfgang Dür,et al.  Efficient quantum communication under collective noise , 2012, Quantum Inf. Comput..

[25]  S. Wehner,et al.  Spatial reference frame agreement in quantum networks , 2013, 1306.5295.

[26]  J. O'Brien,et al.  Demonstration of free-space reference frame independent quantum key distribution , 2013, 1305.0158.

[27]  Shuang Wang,et al.  Proof-of-principle experiment of reference-frame-independent quantum key distribution with phase coding , 2014, Scientific Reports.

[28]  J G Rarity,et al.  Reference-frame-independent quantum-key-distribution server with a telecom tether for an on-chip client. , 2014, Physical review letters.

[29]  Michele Mosca,et al.  Public-key cryptography based on bounded quantum reference frames , 2009, Theor. Comput. Sci..

[30]  G. Vallone,et al.  Free-space quantum key distribution by rotation-invariant twisted photons. , 2014, Physical review letters.

[31]  L. Liang,et al.  Reference-frame-independent quantum key distribution with source flaws , 2015 .

[32]  Stephanie Wehner,et al.  Asynchronous reference frame agreement in a quantum network , 2015, 1505.02565.

[33]  A. Buchleitner,et al.  Quantum teleportation with identical particles , 2015, 1502.05814.

[34]  Jamie Vicary,et al.  Quantum Latin squares and unitary error bases , 2015, Quantum Inf. Comput..

[35]  A. Buchleitner,et al.  Performances and robustness of quantum teleportation with identical particles , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[36]  Jamie Vicary,et al.  Tight Reference Frame-Independent Quantum Teleportation , 2016, QPL.

[37]  Jian-Wei Pan,et al.  Ground-to-satellite quantum teleportation , 2017, Nature.

[38]  Dong He,et al.  Satellite-based entanglement distribution over 1200 kilometers , 2017, Science.

[39]  Jamie Vicary,et al.  Quantum teleportation with infinite reference-frame uncertainty , 2018, Physical Review A.