1,291 research outputs found
Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes
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 (n-1)/2 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 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. 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.Comment: 14 pages, no figure
Multi-party Quantum Computation
We investigate definitions of and protocols for multi-party quantum computing
in the scenario where the secret data are quantum systems. We work in the
quantum information-theoretic model, where no assumptions are made on the
computational power of the adversary. For the slightly weaker task of
verifiable quantum secret sharing, we give a protocol which tolerates any t <
n/4 cheating parties (out of n). This is shown to be optimal. We use this new
tool to establish that any multi-party quantum computation can be securely
performed as long as the number of dishonest players is less than n/6.Comment: Masters Thesis. Based on Joint work with Claude Crepeau and Daniel
Gottesman. Full version is in preparatio
Multiparty quantum secret splitting and quantum state sharing
A protocol for multiparty quantum secret splitting is proposed with an
ordered EPR pairs and Bell state measurements. It is secure and has the
high intrinsic efficiency and source capacity as almost all the instances are
useful and each EPR pair carries two bits of message securely. Moreover, we
modify it for multiparty quantum state sharing of an arbitrary -particle
entangled state based on quantum teleportation with only Bell state
measurements and local unitary operations which make this protocol more
convenient in a practical application than others.Comment: 7 pages, 1 figure. The revision of the manuscript appeared in PLA.
Some procedures for detecting cheat have been added. Then the security
loophole in the original manuscript has been eliminate
Quantum multiparty key distribution protocol without use of entanglement
We propose a quantum key distribution (QKD) protocol that enables three
parties agree at once on a shared common random bit string in presence of an
eavesdropper without use of entanglement. We prove its unconditional security
and analyze the key rate.Comment: 8 pages, no figur
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