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arXiv:0903.4979 · Physical Review A

Relationship between quantum repeating devices and quantum seals

Guang Ping He

Published Jul 8, 2009• 1 citation
arXivHTMLPDF

Abstract

It is revealed that quantum repeating devices and quantum seals have a very close relationship, thus the theory in one field can be applied to the other. Consequently, it is shown that the fidelity bounds and optimality of quantum repeating devices for decoding quantum information can be violated when they are used for decoding classical information from quantum states and the security bounds for protocols sealing quantum data exist.

DOI
10.1103/physreva.80.012308

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It is revealed that quantum repeating devices and quantum seals have a very close relationship, thus the theory in one field can be applied to the other. Consequently, it is shown that the fidelity bounds and optimality of quantum repeating devices for decoding quantum information can be violated when they are used for decoding classical information from quantum states and the security bounds for protocols sealing quantum data exist.
Abstract: A quantum sealing protocol is a quantum cryptographic protocol that can detect unsealing of a message. It is known that quantum bit sealing is insecure. However, this does not imply that quantum string sealing is also insecure. So the possibility of quantum string sealing has been studied. In this paper, we propose a quantum sealing protocol and give an information theoretic analysis. We also show that our protocol is almost optimal for uniformly distributed inputs in the sense that the upper bound of information leaks almost matches the trivial lower bound.
The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability $\ensuremath{\alpha}$, and reading the bit can be detected with the probability $\ensuremath{\beta}$, the upper bounds are $\ensuremath{\beta}\ensuremath{\leqslant}1∕2$ and $\ensuremath{\alpha}+\ensuremath{\beta}\ensuremath{\leqslant}9∕8$.
After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocols is more powerful. We prove for general states but under the assumption of incoherent eavesdropping that Alice and Bob share some so-called intrinsic information in their classical random variables, resulting from optimal measurements, if and only if the parties' quantum systems are entangled. In addition, we provide evidence that the potentials of classical and of quantum protocols are equal in every situation. Consequently, many techniques and results from quantum information theory directly apply to problems in classical information theory, and vice versa. For instance, it was previously believed that two parties can carry out unconditionally secure key agreement as long as they share some intrinsic information in the adversary's view. The analysis of this purely classical problem from the quantum information-theoretic viewpoint shows that this is true in the binary case, but false in general. More explicitly, bound entanglement, i.e., entanglement that cannot be purified by any quantum protocol, has a classical counterpart. This "bound intrinsic information" cannot be distilled to a secret key by any classical protocol. As another application we propose a measure for entanglement based on classical information-theoretic quantities.
Sealing information means making it publicly available, but with the possibility of knowing if it has been read. Commenting on Ref. 1, we will show that perfect quantum sealing is not possible for perfectly retrievable information, due to the possibility of performing a perfect measurement without disturbance, even on unknown states. The measurement is a collective one, and this makes the protocol of quantum sealing very interesting as the only example of the power of collective measurements in breaking security.
Secure multi-party computation (SMC) addresses the problem of jointly computing global functions of private inputs while revealing minimal information about individual data. Two prominent examples of SMC tasks are sealed-bid auction and secure multi-party summation. Existing schemes for quantum auction and quantum summation have largely been developed independently, motivated by distinct applications and employing different computational primitives. In this work, mutual reductions between the two tasks are established for single-item sealed-bid auctions with first-price payment. In one direction, an auction used as a black box computes a secure sum: each party bids a private random key drawn from its input, so the clearing price depends on the inputs only through their sum SSS. The reduction is perfectly private against colluding semi-honest parties and uses O(S2log⁡(1/δ))O(S^2\log(1/δ))O(S2log(1/δ)) auction rounds, which is optimal, or O(Slog⁡(1/δ))O(S\log(1/δ))O(Slog(1/δ)) under coherent access. It can be instantiated with an existing auctioneer-free quantum auction after a one-line change to its disjunction subroutine, which as published leaks occupancy counts. In the other direction, summation with randomized inputs yields threshold disjunctions, and a single search over composite keys locates the highest bid and a winner, revealing nothing else. Because each query consumes the bidders' encodings, a bidder can adapt its effective bid undetected, while a fixed query set restores sealed bidding. Combinatorial auctions and general payment rules lie outside this framework. On a superconducting processor, one instance of each direction is executed, recovering the winner for four-bidder instances with ties and the sum of private inputs from repeated auctions.