Communication channels analogous to one out of two oblivious transfers based on quantum uncertainty

Abstract

This paper proposes a cryptographic quantum communication scheme analogous to one out of two oblivious transfers based on quantum conjugate coding defined in a four-dimensional Hilbert space. The quantum uncertainty principle ensures that our scheme can satisfy the following two conditions: (i) a sender, Bob, can encode two bits of information $X\ensuremath{\in}{0,1}$ and $Y\ensuremath{\in}{0,1},$ but a receiver, Alice, can only obtain either X or Y dependent on her choice; and (ii) honest Bob, who attempts to encode $(X,Y),$ cannot reveal Alice's choice. By contrast, when malicious Bob tries to reveal her choice, honest Alice can detect malicious Bob with a finite probability. Moreover, by using our proposed scheme many times, we can construct a protocol for quantum bit commitment (QBC) from Alice to Bob. Contrary to common belief, the security of our QBC protocol may not be violated by the well-known no-go theorem of QBC. This is because our QBC protocol does not meet the assumptions in which the no-go theorem holds.