A no-summoning theorem in relativistic quantum theory

Alice gives Bob an unknown localized physical state at some point P. At some point Q in the causal future of P, Alice will ask Bob for the state back. Bob knows this, but does not know at which point Q until the request is made. Bob can satisfy Alice’s summons, with arbitrarily short delay, for a quantum state in Galilean space-time or a classical state in Minkowski space-time. However, given an unknown quantum state in Minkowski space-time, he cannot generally fulfil her summons. This no-summoning theorem is a fundamental feature of, and intrinsic to, relativistic quantum theory. It follows from the no-signalling principle and the no-cloning theorem, but not from either alone.

[1]  A. Winter,et al.  Information causality as a physical principle , 2009, Nature.

[2]  Schumacher,et al.  Noncommuting mixed states cannot be broadcast. , 1995, Physical review letters.

[3]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[4]  Adrian Kent,et al.  Secure Classical Bit Commitment Using Fixed Capacity Communication Channels , 1999, Journal of Cryptology.

[5]  Lev Vaidman Instantaneous measurement of nonlocal variables. , 2003, Physical review letters.

[6]  R. Werner,et al.  Optimal cloning of pure states, testing single clones , 1998, quant-ph/9807010.

[7]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[8]  Nicolas J. Cerf,et al.  Highly asymmetric quantum cloning in arbitrary dimension , 2005, Quantum Inf. Comput..

[9]  Horace P. Yuen,et al.  Amplification of quantum states and noiseless photon amplifiers , 1986 .

[10]  G. Lindblad A General No-Cloning Theorem , 1999 .

[11]  E. Schrödinger Discussion of Probability Relations between Separated Systems , 1935, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  N. Gisin,et al.  Multipartite Asymmetric Quantum Cloning , 2005 .

[13]  R. Werner OPTIMAL CLONING OF PURE STATES , 1998, quant-ph/9804001.

[14]  Buzek,et al.  Quantum copying: Beyond the no-cloning theorem. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[15]  Nicolas J. Cerf,et al.  Asymmetric quantum cloning in any dimension , 1998, quant-ph/9805024.

[16]  Marek Czachor,et al.  Mobility and non-separability , 1991 .

[17]  N. Gisin,et al.  Generalised Asymmetric Quantum Cloning , 2005, quant-ph/0505152.

[18]  N. Gisin Stochastic quantum dynamics and relativity , 1989 .

[19]  Adrian Kent,et al.  Quantum Tagging: Authenticating Location via Quantum Information and Relativistic Signalling Constraints , 2010, ArXiv.

[20]  Adrian Kent,et al.  Location-Oblivious Data Transfer with Flying Entangled Qudits , 2011, ArXiv.

[21]  D. Dieks Communication by EPR devices , 1982 .

[22]  Alain Aspect,et al.  Speakable and Unspeakable in Quantum Mechanics: Free variables and local causality , 2004 .

[23]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[24]  Adrian Kent Nonlinearity without superluminality , 2005 .

[25]  Rafail Ostrovsky,et al.  Position-Based Quantum Cryptography: Impossibility and Constructions , 2011, IACR Cryptol. ePrint Arch..

[26]  Hoi-Kwong Lo,et al.  Is Quantum Bit Commitment Really Possible? , 1996, ArXiv.

[27]  Nicolas Gisin,et al.  Weinberg's non-linear quantum mechanics and supraluminal communications , 1990 .

[28]  D. Bruß,et al.  Optimal Universal Quantum Cloning and State Estimation , 1997, quant-ph/9712019.

[29]  J. Bell,et al.  The Theory of Local Beables , 1975 .

[30]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[31]  Robert A. Malaney,et al.  Location-dependent communications using quantum entanglement , 2010, 1003.0949.

[32]  S. Iblisdir Multipartite asymmetric quantum cloning (4 pages) , 2005 .

[33]  Dominic Mayers Unconditionally secure quantum bit commitment is impossible , 1997 .

[34]  Yuen,et al.  Impossibility of measuring the wave function of a single quantum system. , 1996, Physical review letters.

[35]  S. Massar,et al.  Optimal Quantum Cloning Machines , 1997, quant-ph/9705046.

[36]  Robert A. Malaney,et al.  Quantum Location Verification in Noisy Channels , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[37]  S. Braunstein,et al.  Impossibility of deleting an unknown quantum state , 2000, Nature.

[38]  Adrian Kent,et al.  Unconditionally secure bit commitment with flying qudits , 2011, ArXiv.

[39]  Samuel L. Braunstein,et al.  Quantum-information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit , 2001 .

[40]  Richard Jozsa A stronger no-cloning theorem , 2002 .

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

[42]  Serge Fehr,et al.  Position-Based Quantum Cryptography , 2011, ERCIM News.