Oblivious transfer and quantum channels as communication resources
Tóm tắt
We show that from a communication-complexity perspective, the primitive called oblivious transfer—which was introduced in a cryptographic context—can be seen as the classical analogue to a quantum channel in the same sense as non-local boxes are of maximally entangled qubits. More explicitly, one realization of non-cryptographic oblivious transfer allows for the perfect simulation of sending one qubit and measuring it in an orthogonal basis. On the other hand, a qubit channel allows for realizing non-cryptographic oblivious transfer with probability roughly 85 %, whereas 75 % is the classical limit.
Tài liệu tham khảo
Ambainis A, Nayak A, Ta-Shma A, Vazirani U (1998) Dense quantum coding and a lower bound for 1-way quantum automata. quant-ph/9804043
Bell JS (1964) On the Einstein–Podolsky–Rosen paradox. Physics 1:195–200
Bennett CH, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W (1993) Teleporting an unknown quantum state via dual classical and EPR channels. Phys Rev Lett 70:1895–1899
Buhrman H, Christandl M, Unger F, Wehner S, Winter A (2006) Implications of superstrong nonlocality for cryptography. Proc R Soc A 462(2071):1919–1932, quant-ph/0504133
Cerf N, Gisin N, Massar S (2000) Classical teleportation of a quantum bit. Phys Rev Lett 84(11):2521–2524
Cerf N, Gisin N, Massar S, Popescu S (2005) Simulating maximal quantum entanglement without communication. Phys Rev Lett 94:220403
Devetak I, Harrow AW, Winter AJ (2004) A family of quantum protocols. Phys Rev Lett 93(23):230504
Devetak I, Harrow AW, Winter AJ (2008) A resource framework for quantum Shannon theory. IEEE Trans Inf Theory 54(10):4587–4618
Einstein A, Podolsky B, Rosen N (1935) Can quantum-mechanical description of physical reality be considered complete? Phys Rev 41:777–780
Gleason AM (1957) Measures on the closed subspaces of a Hilbert space. J Math Mech 6:885
Jauch JM, Piron C (1963) Can hidden variables be excluded in quantum mechanics? Helv Phys Acta 36:827
Kochen S, Specker E (1967) The problem of hidden variables in quantum mechanics. J Math Mech 17(1):59–87
Popescu S, Rohrlich D (1994) Quantum nonlocality as an axiom. Found Phys 24:379–385
Rabin M (1981) How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory
Specker E (1960) Die Logik nicht gleichzeitig entscheidbarer Aussagen. Dialectica 14:239–246
Toner B, Bacon D (2003) Communication cost of simulating Bell correlations. Phys Rev Lett 91(18):187904
von Neumann J (1955) Mathematische Grundlagen der Quanten-Mechanik. Verlag Julius-Springer, Berlin, 1932. Mathematial foundations of quantum mechanics. Princeton University, Princeton
Wiesner S (1983) Conjugate coding. Sigact News 15(1):78–88
Wolf S, Wullschleger J (2006) Oblivious transfer is symmetric. In: Advances in cryptology—EUROCRYPT ’06, volume 4004 of Lecture Notes in Computer Science. Springer, pp 222–232