Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414-3417, 1996.  Home/Search   Document Not in Database   Summary   APS   Related Articles   Check

....concealing that Bob has no reasonable way of obtaining any information on Alice s commitment before she discloses it. Since Bennett and Brassard [1] proposed the quantum key exchange protocol, various quantum cryptographic protocols including bit commitment have been investigated. However, Mayers [8] proved that any quantum bit commitment scheme can either be defeated by Alice or Bob as long as both have unrestricted quantum computational power. # Supported in part by Grant in Aid for Scientific Research, Ministry of Education, Culture, Sports, Science, and Technology, 14780190 This does ....

....1 respectively, and are two orthogonal states of an extra ancilla kept by Alice. In this case, Alice can unveil x 0 and x 1 with some non zero probability, i.e. S 0 (n) 0 and S 1 (n) 0. The binding condition that S 0 (n) 0 or S 1 (n) 0 is too strong was previously noticed by Mayers [8], and Dumais, Mayers, and Salvail [4] proposed the weaker condition S 0 (n) S 1 (n) 1 #(n) where #(n) is negligible (i.e. smaller than 1 poly(n) for any polynomial poly(n) In this paper, we also follow this condition, and call a bit commitment scheme statistically binding if it satisfies ....

Mayers, D. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters 78, 17 (1997), 3414--3417.

....the commitment. We say a bit commitment protocol is binding if Alice is unable to change her mind and concealing if Bob cannot determine b before the opening of the commitment. A cold rain fell on the scientific community when unconditional security for quantum bit commitment was proven impossible [19, 20, 18]. Though unconditional security was impossible, one could still hope to base the security of quantum bit commitment on a computational assumption. A quantum one way function must be easy to compute with a quantum computer but hard to invert even using quantum computations. Since there is a ....

Mayers, D., "Unconditionally Secure Quantum Bit Commitment is Impossible", Physical Review Letters, vol. 78, no 17, April 1997, pp. 3414 -- 3417.

.... 27] and exponentially more efficient quantum than classical communication complexity protocols [24] Equally important for understanding the power of quantum models are upper bounds and impossibility proofs, such as the containment of BQP in PP [1, 8] the impossibility of quantum bit commitment [20], and the existence of oracles relative to which quantum computers have limited power [3, 8] In this paper we consider the potential advantages of quantum variants of zero knowledge proof systems. Zeroknowledge proof systems were first defined by Goldwasser, Micali, and Rackoff [14] in 1985, ....

D. Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414--3417, 1997.

....string commitment satisfying a weak computational binding property. keywords: quantum bit commitment, oblivious transfer, quantum measurement, computational assumptions. 1 Introduction As for the classical case, secure quantum 2 party cryptography must rely upon some kind of assumption[14, 15, 13]. However, the two models of computation do not share the same capabilities and limits[11, 6, 20] In particular, given a classical black box for bit commitment, there exists a quantum protocol, called the CK protocol [6, 5, 4] achieving 1 2 oblivious transfer (one out of two oblivious transfer) ....

Mayers, D., Unconditionally Secure Quantum Bit Commitment is Impossible, Physical Review Letters, vol. 78, no 17, April 1997, pp. 34143417.

....applications. For example, computational zero knowledge proofs [8, 9] can be constructed from binding commitments whereas perfect zero knowledge arguments [4] use concealing commitments. In quantum cryptography, computational assumptions are also required for bit commitment and oblivious transfer [15, 16, 14]. The standard computational assumptions for the quantum case are de ned as in the classical case except that they must resist quantum inverters. A quantum one way function is simply a classical function f : f0; 1g f0; 1g l(n) for which given any x 2 f0; 1g , f(x) can be eciently ....

Mayers, D., \Unconditionally Secure Quantum Bit Commitment is Impossible", Physical Review Letters, vol. 78, no 17, April 1997, pp. 3414 - 3417.

....For example, computational zero knowledge proofs [8, 9] can be constructed from binding commitments whereas perfect zero knowledge arguments [4] use con cealing commitments. In quantum cryptography, computational assumptions are also required for bit commitment and oblivious transfer [15, 16, 14]. The standard computational assumptions for the quantum case are defined as in the classical case except that they must resist quantum inverters. A quantum one way function is simply a clas sical function f: 0, 1 n 0, 1 l(n) for which given any x e 0, 1 n, f(x) Can be efficiently ....

MAYERS, D., "Unconditionally Secure Quantum Bit Commitment is Impossible", Physical Review Letters, vol. 78, no 17, April 1997, pp. 3414-3417.

....R is some additional space used to purify the random path V 1 ; V t 1 (resp. V 1 ; V t ) We employ the following fact from [22] the local transition theorem ) The fact is a variation of the impossibility result for unconditionally secure quantum bit commitment due to Mayers [21] and Lo and Chau [20] Fact 6 Let 1 ; 2 be two density matrices with support in a Hilbert space H, K a Hilbert space of dimension at least dimH, and j 1 i; j 2 i; any puri cations of 1 resp. 2 in K. Then there is a puri cation j 2 i of 2 in K, that is obtained by applying a ....

D. Mayers. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett., vol.78, pp.3414-3417, 1997.

....where the adversary is one of the participants in the system and not an outside eavesdropper, much less is known. Some proofs were also attempted for tasks such as bit commitment [BCJL93] but those proofs were later discovered to be awed, since bit commitment was proven impossible [May96, LC97a, May97, LC96, LC97b, BCMS98] There have also been several works on quanutm coin tossing. Although arbitrarily small error is known to be impossible, several works have focused on reducing the error as much as possible [LC96, MS99, ATVY00, Amb01] Yet another line of work has focused on how to achieve ....

Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414-3417, 1997. quant-ph/9605044.

....give a direct proof of the Average encoding theorem in case of the uniform distribution on X, without using Lindblad Uhlmann monotonicity, with the constant 2 ln 2 replaced with the somewhat weaker constant 4. Another primitive we use is derived from the work of Lo and Chau [17] and Mayers [18], and combines results of Jozsa [19] and Fuchs and van de Graaf [20] Consider two bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with signi cant probability. Then the other party can locally transform any of the states to a state ....

....bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with signi cant probability. Then the other party can locally transform any of the states to a state that is close to the other. Theorem I. 6 (Local transition theorem) based on [17] [18], 19] 20] Let 1 ; 2 be two mixed states with support in a Hilbert space H, K any Hilbert space of dimension at least dim(H) and j i i any puri cations of i in K. Then, there is a local unitary transformation U on K that maps j 2 i to j 2 i = I U j 2 i such that 2 j k t ....

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D. Mayers, \Unconditionally secure quantum bit commitment is impossible," Physical review letters, vol. 78, pp. 3414-3417, 1997.

....Now Bob s system is with probability 1 2 in the state j i, and with probability half in the state ji, and the register A re ects the result Bob gets, i.e. Alice knows whether Bob gets j i or ji. Notice that Bob s reduced density matrix is the same in both cases. An important Theorem by Mayers [6] and independently Lo and Chau [5] states: Theorem 4. Suppose the reduced density matrix of B is the same in AB and AB . Then Alice can move from AB to AB by applying a local transformation on her side. i.e. even though Alice can not change Bob s reduced density matrix, she can determine how ....

D. Mayers. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett., 78:3414-3417, 1997.

....encoding # (corresponding to a random string) is on average a good approximation of any encoded state. Thus, in certain situations, we may dispense with the encoding altogether, and use the single state # instead. We also use another primitive derived from the work of Lo and Chau [14] and Mayers [15] which combines results of Jozsa [10] and Fuchs and van de Graaf [8] Consider two bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with significant probability. Then the other party can locally transform any of the states to a state ....

....two bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with significant probability. Then the other party can locally transform any of the states to a state that is close to the other. Theorem 1. 4 (Local transition theorem) based on [14, 15, 10, 8]) Let # 1 , # 2 be two mixed states with support in a Hilbert space H, K any Hilbert space of dimension at least dim(H) and # i # any purifications of # i in H# K. Then, there is a local unitary transformation U on K that maps # 2 # to # # 2 # = I# U # 2 # such that # ....

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D. Mayers. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett., 78:3414--3417, 1997.

....I(Q : X) S(#QX #Q# #X ) we get the average encoding theorem as a special case. This more general theorem seems to be of independent interest. A classical version of the theorem can be found in, e.g. 9] We also use another primitive derived from the work of Lo and Chau [17] and Mayers [18] which combines results of Jozsa [12] and Fuchs and van de Graaf [11] Consider two bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with significant probability. Then the other party can locally transform any of the states to a state ....

....two bi partite pure states such that one party sharing the states cannot locally distinguish between the two states with significant probability. Then the other party can locally transform any of the states to a state that is close to the other. Theorem 1. 6 (Local transition theorem) based on [17, 18, 12, 11]) Let #1 , #2 be two mixed states with support in a Hilbert space H, K any Hilbert space of dimension at least dim(H) and # i # any purifications of # i in H# K. Then, there is a local unitary transformation U on K that maps #2# to # # 2 # = I# U #2# such that # # #1 ....

[Article contains additional citation context not shown here]

D. Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414--3417, 1997.

....being incompatible with classical information theory indicates that quantum cryptography is more powerful than its classical counterpart. However, quantum information has also fundamental limits when cryptography between two potentially collaborative but untrusted parties is considered. Mayers [13] has proven that any quantum bit commitment scheme can either be defeated by the committer or the receiver as long as both sides have unrestricted quantum computational power. Mayers general result was built upon previous works of Mayers [11] and Lo and Chau [9] However, the no go theorem does ....

....case, for both value of w # 0, 1 , the opening circuit O n w can put HOpen into a mixture that will unveil w successfully with some non zero probability. So we have S 0 (n) S 1 (n) 0. The fact that the binding condition S 0 (n) 0 #S 1 (n) 0 is too strong was previously noticed in [13]. We propose the weaker condition S 0 (n) S 1 (n) 1 # #(n) where #(n) is negligible (i.e. smaller than 1 poly(n) for any polynomial p(n) For classical applications, this binding condition (with #(n) 0) is as good as if the commiter was forced to honestly commit a random bit (with the ....

Mayers, D., "Unconditionally Secure Quantum Bit Commitment is Impossible", Physical Review Letters, vol. 78, no 17, April 1997, pp. 3414 -- 3417.

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Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414-3417, 1996.

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D. Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414--3417, April 1997.

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D. Mayers. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett., (78):3414--3417, 1997.

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D. Mayers, "Unconditionally Secure Quantum Bit Commitment is Impossible," Phys. Rev. Lett. 78, 3414 (1997).

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D. Mayers, Unconditionally Secure Quantum Bit Commitment is Impossible, Los Alamos preprint archive quant-ph/9605044, January 97.

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D. Mayers, "Unconditionally secure quantum bit commitment is impossible," Physical review letters, vol. 78, pp. 3414--3417, 1997.

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D. Mayers, Unconditionally secure quantum bit commitment is impossible , Phys. Rev. Letters, vol. 78, no. 17, pp. 34143417, 1997.

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D. Mayers, Unconditionally secure quantum bit commitment is impossible, Phys. Rev. Letters, vol.78, 1997, pp. 3414-3417.

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D. Mayers, "Unconditionally secure quantum bit commitment is impossible," Physical review letters, vol. 78, pp. 3414--3417, 1997.

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Mayers, D. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters 78, 17 (1997), 3414--3417.

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Mayers, D., "Unconditionally Secure Quantum Bit Commitment is Impossible", Physical Review Letters, vol. 78, no 17, April 1997, pp. 3414 -- 3417.

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D. Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78:3414-3417, 1997.

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