29,096 research outputs found
A Universal Two--Bit Gate for Quantum Computation
We prove the existence of a class of two--input, two--output gates any one of
which is universal for quantum computation. This is done by explicitly
constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A
{\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit
gate.Comment: 3 pages, RevTeX, two figures in a uuencoded fil
Quantum computers can search arbitrarily large databases by a single query
This paper shows that a quantum mechanical algorithm that can query
information relating to multiple items of the database, can search a database
in a single query (a query is defined as any question to the database to which
the database has to return a (YES/NO) answer). A classical algorithm will be
limited to the information theoretic bound of at least O(log N) queries (which
it would achieve by using a binary search).Comment: Several enhancements to the original pape
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
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
Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for
quantum key distribution. We first give a key distribution protocol based on
entanglement purification, which can be proven secure using methods from Lo and
Chau's proof of security for a similar protocol. We then show that the security
of this protocol implies the security of BB84. The entanglement-purification
based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these
codes are used to remove the use of quantum computation from the Lo-Chau
protocol.Comment: 5 pages, Latex, minor changes to improve clarity and fix typo
Semi-dynamic connectivity in the plane
Motivated by a path planning problem we consider the following procedure.
Assume that we have two points and in the plane and take
. At each step we add to a compact convex
set that does not contain nor . The procedure terminates when the sets
in separate and . We show how to add one set to
in amortized time plus the time needed to find
all sets of intersecting the newly added set, where is the
cardinality of , is the number of sets in
intersecting the newly added set, and is the inverse of the
Ackermann function
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
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
Quantum key distribution via quantum encryption
A quantum key distribution protocol based on quantum encryption is presented
in this Brief Report. In this protocol, the previously shared
Einstein-Podolsky-Rosen pairs act as the quantum key to encode and decode the
classical cryptography key. The quantum key is reusable and the eavesdropper
cannot elicit any information from the particle Alice sends to Bob. The concept
of quantum encryption is also discussed.Comment: 4 Pages, No Figure. Final version to appear in PR
Quantifying nonorthogonality
An exploratory approach to the possibility of analyzing nonorthogonality as a
quantifiable property is presented. Three different measures for the
nonorthogonality of pure states are introduced, and one of these measures is
extended to single-particle density matrices using methods that are similar to
recently introduced techniques for quantifying entanglement. Several
interesting special cases are considered. It is pointed out that a measure of
nonorthogonality can meaningfully be associated with a single mixed quantum
state. It is then shown how nonorthogonality can be unlocked with classical
information; this analysis reveals interesting inequalities and points to a
number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.
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