30,462 research outputs found
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
On the origin of noisy states whose teleportation fidelity can be enhanced through dissipation
Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy
states whose teleportation fidelity can be enhanced by subjecting one of the
qubits to dissipative interaction with the environment via amplitude damping
channel (ADC). We show that such noisy states result while sharing the states
(| \Phi ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show
that under similar dissipative interactions different Bell states give rise to
noisy entangled states that are qualitatively very different from each other in
the sense, only the noisy entangled states constructed from the Bell states (|
\Phi ^{\pm}>) can \emph{}be made better sometimes by subjecting the unaffected
qubit to a dissipative interaction with the environment. Importantly if the
noisy state is non teleporting then it can always be made teleporting with this
prescription. We derive the most general restrictions on improvement of such
noisy states assuming that the damping parameters being different for both the
qubits. However this curious prescription does not work for the noisy entangled
states generated from (| \Psi ^{\pm}> =\frac{1}{\sqrt{2}}(| 01> \pm | 10>)).
This shows that an apriori knowledge of the noisy channel might be helpful to
decide which Bell state needs to be shared between Alice and Bob. \emph{}Comment: Latex, 18 pages: Revised version with a new result. Submitted to PR
Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations
We introduce a new class of quantum quantum key distribution protocols,
tailored to be robust against photon number splitting (PNS) attacks. We study
one of these protocols, which differs from the BB84 only in the classical
sifting procedure. This protocol is provably better than BB84 against PNS
attacks at zero error.Comment: 4 pages, 2 figure
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
Quantum key distribution with 2-bit quantum codes
We propose a prepare-and-measure scheme for quantum key distribution with
2-bit quantum codes. The protocol is unconditionally secure under whatever type
of intercept-and-resend attack. Given the symmetric and independent errors to
the transmitted qubits, our scheme can tolerate a bit error rate up to 26% in
4-state protocol and 30% in 6-state protocol, respectively. These values are
higher than all currently known threshold values for prepare-and-measure
protocols. A specific realization with linear optics is given.Comment: Approved for publication in Physical Review Letter
Irreversibility in asymptotic manipulations of entanglement
We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states
under pure entanglement catalytic LOCC adde
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
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
An improved bound on distillable entanglement
The best bound known on 2-locally distillable entanglement is that of Vedral
and Plenio, involving a certain measure of entanglement based on relative
entropy. It turns out that a related argument can be used to give an even
stronger bound; we give this bound, and examine some of its properties. In
particular, and in contrast to the earlier bounds, the new bound is not
additive in general. We give an example of a state for which the bound fails to
be additive, as well as a number of states for which the bound is additive.Comment: 14 pages, no figures. A significant erratum in theorems 4 and 5 has
been fixe
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