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H.P. Yuen
Quantum
Physics, quant-ph/0109055
Abstract
Bit commitment
involves the submission of evidence from one party to another so that
the evidence can be used to confirm a later revealed bit value by
the first party, while the second party cannot determine the bit value
from the evidence alone. It is widely believed that unconditionally
secure quantum bit commitment is impossible due to quantum entanglement
cheating, which is codified in a general impossibility theorem. In
this paper, the scope of this general impossibility proof is analyzed,
and gaps are found. Two variants of a bit commitment scheme utilizing
anonymous quantum states and decoy states are presented. In the first
variant, the exact verifying measurement is independent of the committed
bit value, thus the second party can make it before the first party
opens, making possible an unconditional security proof based on no-cloning.
In the second variant, the impossibility proof fails because quantum
entanglement purification of a mixed state does not render the protocol
determinate. Whether impossibility holds in this or similar protocols
is an open question, although preliminary results already show that
the impossibility proof cannot work as it stands.
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