2,840 research outputs found
Quantum secret sharing with qudit graph states
We present a unified formalism for threshold quantum secret sharing using
graph states of systems with prime dimension. We construct protocols for three
varieties of secret sharing: with classical and quantum secrets shared between
parties over both classical and quantum channels.Comment: 13 pages, 12 figures. v2: Corrected to reflect imperfections of (n,n)
QQ protocol. Also changed notation from to , corrected typos,
updated references, shortened introduction. v3: Updated acknowledgement
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
Efficient sharing of a continuous-variable quantum secret
We propose an efficient scheme for sharing a continuous variable quantum
secret using passive optical interferometry and squeezers: this efficiency is
achieved by showing that a maximum of two squeezers is required to replicate
the secret state, and we obtain the cheapest configuration in terms of total
squeezing cost. Squeezing is a cost for the dealer of the secret as well as for
the receivers, and we quantify limitations to the fidelity of the replicated
secret state in terms of the squeezing employed by the dealer.Comment: 7 pages, 3 figure
Random coding for sharing bosonic quantum secrets
We consider a protocol for sharing quantum states using continuous variable
systems. Specifically we introduce an encoding procedure where bosonic modes in
arbitrary secret states are mixed with several ancillary squeezed modes through
a passive interferometer. We derive simple conditions on the interferometer for
this encoding to define a secret sharing protocol and we prove that they are
satisfied by almost any interferometer. This implies that, if the
interferometer is chosen uniformly at random, the probability that it may not
be used to implement a quantum secret sharing protocol is zero. Furthermore, we
show that the decoding operation can be obtained and implemented efficiently
with a Gaussian unitary using a number of single-mode squeezers that is at most
twice the number of modes of the secret, regardless of the number of players.
We benchmark the quality of the reconstructed state by computing the fidelity
with the secret state as a function of the input squeezing.Comment: Updated figure 1, added figure 2, closer to published versio
- …