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arXiv:quant-ph/0305142

A simple unconditionally secure quantum bit commitment protocol via quantum teleportation

Horace P. Yuen

Published May 23, 2003• 3 citations
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Abstract

By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.

DOI
10.48550/arxiv.quant-ph/0305142

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In a secure bit commitment protocol involving only classical physics, A commits either a $0$ or a $1$ to B. If quantum information is used in the protocol, A may be able to commit a state of the form $\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉.$ If so, she can also commit mixed states in which the committed bit is entangled with other quantum states under her control. We introduce here a quantum cryptographic primitive, bit commitment with a certificate of classicality (BCCC), which differs from standard bit commitment in that it guarantees that the committed state has a fixed classical value. We show that no unconditionally secure BCCC protocol based on special relativity and quantum theory exists. We also propose complete definitions of security for quantum and relativistic bit commitment.

arXiv:quant-ph/9910087•Physical Review A•Mar 2, 2000•23 citations
By using local quantum teleportation of a fixed state to one qubit of an entangled pair sent from the other party, it is shown how one party can commit a bit with only classical information as evidence that results in an unconditionally secure protocol. The well-known ``impossibility proof'' does not cover such protocols due to its different commitment and opening prescriptions, which necessitate actual quantum measurements among different possible systems that cannot be entangled as a consequence.
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.
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 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 extended and analyzed, and gaps are found. Three specific protocols are described for which the entanglement cheating as given in the impossibility proof fails to work. One of these protocols, QBC2, is proved to be unconditionally secure.
It is shown how the evidence state space in quantum bit commitment may be made to depend on the bit value 0 or 1 with split entangled pairs. As a consequence, one can obtain a protocol that is perfectly concealing, but is also εεε-binding because the bit-value dependent evidence space prevents the committing party from cheating by means of a local transformation that is independent of the part of evidence state space that has never been in his possession.
The commitment of bits between two mutually distrustful parties is a powerful cryptographic primitive with which many cryptographic objectives can be achieved. 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. Gaps in the proof of this impossibility theorem are found. An unconditionally secure bit commitment protocol utilizing anonymous quantum states and the no-clone theorem is presented below with a full security proof.
In a secure bit commitment protocol involving only classical physics, A commits either a 000 or a 111 to B. If quantum information is used in the protocol, A may be able to commit a state of the form $\ensuremath{\alpha}|0〉+\ensuremath{\beta}|1〉.$ If so, she can also commit mixed states in which the committed bit is entangled with other quantum states under her control. We introduce here a quantum cryptographic primitive, bit commitment with a certificate of classicality (BCCC), which differs from standard bit commitment in that it guarantees that the committed state has a fixed classical value. We show that no unconditionally secure BCCC protocol based on special relativity and quantum theory exists. We also propose complete definitions of security for quantum and relativistic bit commitment.