Can quantum cryptography imply quantum mechanics?

It has been suggested that the ability of quantum mechanics to allow secure distributionof secret key together with its inability to allow bit commitment or communicate superluminallymight be sufficient to imply the rest of quantum mechanics. I argue using atoy theory as a counterexample that this is not the case. I further discuss whether anadditional axiom (key storage) brings back the quantum nature of the theory.

[1]  Larry Carter,et al.  New Hash Functions and Their Use in Authentication and Set Equality , 1981, J. Comput. Syst. Sci..

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

[3]  R. Spekkens.  Evidence for the epistemic view of quantum states: A toy theory , 2004, quant-ph/0401052.

[4]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[5]  Charles H. Bennett,et al.  Quantum cryptography without Bell's theorem. , 1992, Physical review letters.

[6]  C. Fuchs.  Quantum Mechanics as Quantum Information (and only a little more) , 2002, quant-ph/0205039.

[7]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[8]  Jeffrey Bub,et al.  Characterizing Quantum Theory in Terms of Information-Theoretic Constraints , 2002 .

[9]  D. M. Appleby.  The Bell–Kochen–Specker theorem , 2003, quant-ph/0308114.

[10]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

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

[12]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

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

[14]  Jeffrey Bub,et al.  The Quantum Bit Commitment Theorem , 2000, quant-ph/0007090.

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

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

[17]  Andrew Chi-Chih Yao,et al.  Quantum cryptography with imperfect apparatus , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[18]  Dominic Mayers,et al.  Unconditional security in quantum cryptography , 1998, JACM.

[19]  Andrew Chi-Chih Yao,et al.  Self testing quantum apparatus , 2004, Quantum Inf. Comput..

[20]  Kurt Jacobs,et al.  Information-tradeoff relations for finite-strength quantum measurements , 2001 .