Quantum gambling using two nonorthogonal states

A new (remote) quantum gambling scheme that makes use of the fact that nonorthogonal states cannot be distinguished with certainty is presented. In this scheme, two participants Alice and Bob can be regarded as playing a game of making guesses on identities of quantum states that are in one of two given nonorthogonal states: if Bob makes a correct (an incorrect) guess on the identity of a quantum state that Alice has sent, he wins (loses). It is shown that the scheme is secure against the non-entanglement attack. Heuristically, the scheme is secure in the case of the entanglement attack.