Book
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes.
| Title: | Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes. |
|---|---|
| Authors: | Cramer, Ronald, Crépeau, Claude, Gottesman, Daniel, Smith, Adam |
| Source: | Advances in Cryptology - EUROCRYPT 2005; 2005, p285-301, 17p |
| Abstract: | It is a standard result in the theory of quantum error- correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to arbitrary errors with fidelity exponentially close to 1, at the price of increasing the size of the registers (i.e., the coding alphabet). This demonstrates a sharp distinction between exact and approximate quantum error correction. The codes have the property that any t components reveal no information about the message, and so they can also be viewed as error-tolerant secret sharing schemes. The construction has several interesting implications for cryptography and quantum information theory. First, it suggests that secret sharing is a better classical analogue to quantum error correction than is classical error correction. Second, it highlights an error in a purported proof that verifiable quantum secret sharing (VQSS) is impossible when the number of cheaters t is n/4. In particular, the construction directly yields an honest-dealer VQSS scheme for . We believe the codes could also potentially lead to improved protocols for dishonest-dealer VQSS and secure multi-party quantum computation. More generally, the construction illustrates a difference between exact and approximate requirements in quantum cryptography and (yet again) the delicacy of security proofs and impossibility results in the quantum model. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances in Cryptology - EUROCRYPT 2005 is the property of Springer eBooks and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| DOI: | 10.1007/11426639_17 |
| Database: | Supplemental Index |
Availability