29,630 research outputs found
Fault tolerant quantum key distribution protocol with collective random unitary noise
We propose an easy implementable prepare-and-measure protocol for robust
quantum key distribution with photon polarization. The protocol is fault
tolerant against collective random unitary channel noise. The protocol does not
need any collective quantum measurement or quantum memory. A security proof and
a specific linear optical realization using spontaneous parametric down
conversion are given.Comment: Accepted by PRA as a Rapid Communicatio
When only two thirds of the entanglement can be distilled
We provide an example of distillable bipartite mixed state such that, even in
the asymptotic limit, more pure-state entanglement is required to create it
than can be distilled from it. Thus, we show that the irreversibility in the
processes of formation and distillation of bipartite states, recently proved in
[G. Vidal, J.I. Cirac, Phys. Rev. Lett. 86, (2001) 5803-5806], is not limited
to bound-entangled states.Comment: 4 pages, revtex, 1 figur
The Parity Bit in Quantum Cryptography
An -bit string is encoded as a sequence of non-orthogonal quantum states.
The parity bit of that -bit string is described by one of two density
matrices, and , both in a Hilbert space of
dimension . In order to derive the parity bit the receiver must
distinguish between the two density matrices, e.g., in terms of optimal mutual
information. In this paper we find the measurement which provides the optimal
mutual information about the parity bit and calculate that information. We
prove that this information decreases exponentially with the length of the
string in the case where the single bit states are almost fully overlapping. We
believe this result will be useful in proving the ultimate security of quantum
crytography in the presence of noise.Comment: 19 pages, RevTe
A classical analogue of entanglement
We show that quantum entanglement has a very close classical analogue, namely
secret classical correlations. The fundamental analogy stems from the behavior
of quantum entanglement under local operations and classical communication and
the behavior of secret correlations under local operations and public
communication. A large number of derived analogies follow. In particular
teleportation is analogous to the one-time-pad, the concept of ``pure state''
exists in the classical domain, entanglement concentration and dilution are
essentially classical secrecy protocols, and single copy entanglement
manipulations have such a close classical analog that the majorization results
are reproduced in the classical setting. This analogy allows one to import
questions from the quantum domain into the classical one, and vice-versa,
helping to get a better understanding of both. Also, by identifying classical
aspects of quantum entanglement it allows one to identify those aspects of
entanglement which are uniquely quantum mechanical.Comment: 13 pages, references update
Thermodynamics and the Measure of Entanglement
We point out formal correspondences between thermodynamics and entanglement.
By applying them to previous work, we show that entropy of entanglement is the
unique measure of entanglement for pure states.Comment: 8 pages, RevTeX; edited for clarity, additional references, to appear
as a Rapid Communication in Phys. Rev.
Entanglement Swapping Chains for General Pure States
We consider entanglement swapping schemes with general (rather than
maximally) entangled bipartite states of arbitary dimension shared pairwise
between three or more parties in a chain. The intermediate parties perform
generalised Bell measurements with the result that the two end parties end up
sharing a entangled state which can be converted into maximally entangled
states. We obtain an expression for the average amount of maximal entanglement
concentrated in such a scheme and show that in a certain reasonably broad class
of cases this scheme is provably optimal and that, in these cases, the amount
of entanglement concentrated between the two ends is equal to that which could
be concentrated from the weakest link in the chain.Comment: 18 pages, 5 figure
A Foundation of Programming a Multi-Tape Quantum Turing machine
The notion of quantum Turing machines is a basis of quantum complexity
theory. We discuss a general model of multi-tape, multi-head Quantum Turing
machines with multi final states that also allow tape heads to stay still.Comment: A twelve page version is to appear in the Proceedings of the 24th
International Symposium on Mathematical Foundations of Computer Science in
September, 1999. LNC
Quantum privacy amplification and the security of quantum cryptography over noisy channels
Existing quantum cryptographic schemes are not, as they stand, operable in
the presence of noise on the quantum communication channel. Although they
become operable if they are supplemented by classical privacy-amplification
techniques, the resulting schemes are difficult to analyse and have not been
proved secure. We introduce the concept of quantum privacy amplification and a
cryptographic scheme incorporating it which is provably secure over a noisy
channel. The scheme uses an `entanglement purification' procedure which,
because it requires only a few quantum Controlled-Not and single-qubit
operations, could be implemented using technology that is currently being
developed. The scheme allows an arbitrarily small bound to be placed on the
information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig
macro
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