35,174 research outputs found
A Method of Areas for Manipulating the Entanglement Properties of One Copy of a Two-Particle Pure State
We consider the problem of how to manipulate the entanglement properties of a
general two-particle pure state, shared between Alice and Bob, by using only
local operations at each end and classical communication between Alice and Bob.
A method is developed in which this type of problem is found to be equivalent
to a problem involving the cutting and pasting of certain shapes along with a
certain colouring problem. We consider two problems. Firstly we find the most
general way of manipulating the state to obtain maximally entangled states.
After such a manipulation the entangled state |11>+|22>+....|mm> is obtained
with probability p_m. We obtain an expression for the optimal average
entanglement. Also, some results of Lo and Popescu pertaining to this problem
are given simple geometric proofs. Secondly, we consider how to manipulate one
two particle entangled pure state to another with certainty. We derive
Nielsen's theorem (which states the necessary and sufficient condition for this
to be possible) using the method of areas.Comment: 29 pages, 9 figures. Section 2.4 clarified. Error in second colouring
theorem (section 3.2) corrected. Some other minor change
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.
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 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
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
Indeterminate-length quantum coding
The quantum analogues of classical variable-length codes are
indeterminate-length quantum codes, in which codewords may exist in
superpositions of different lengths. This paper explores some of their
properties. The length observable for such codes is governed by a quantum
version of the Kraft-McMillan inequality. Indeterminate-length quantum codes
also provide an alternate approach to quantum data compression.Comment: 32 page
Quantum Key Distribution Using Quantum Faraday Rotators
We propose a new quantum key distribution (QKD) protocol based on the fully
quantum mechanical states of the Faraday rotators. The protocol is
unconditionally secure against collective attacks for multi-photon source up to
two photons on a noisy environment. It is also robust against impersonation
attacks. The protocol may be implemented experimentally with the current
spintronics technology on semiconductors.Comment: 7 pages, 7 EPS 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
Mixed State Entanglement and Quantum Error Correction
Entanglement purification protocols (EPP) and quantum error-correcting codes
(QECC) provide two ways of protecting quantum states from interaction with the
environment. In an EPP, perfectly entangled pure states are extracted, with
some yield D, from a mixed state M shared by two parties; with a QECC, an arbi-
trary quantum state can be transmitted at some rate Q through a
noisy channel without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state (obtained
by sharing halves of EPR pairs through a channel ) yields a QECC on
with rate , and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
and that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for when is Bell-diagonal. While EPPs require classical communica-
tion, QECCs do not, and we prove Q is not increased by adding one-way classical
communication. However, both D and Q can be increased by adding two-way com-
munication. We show that certain noisy quantum channels, for example a 50%
depolarizing channel, can be used for reliable transmission of quantum states
if two-way communication is available, but cannot be used if only one-way com-
munication is available. We exhibit a family of codes based on universal hash-
ing able toachieve an asymptotic (or ) of 1-S for simple noise models,
where S is the error entropy. We also obtain a specific, simple 5-bit single-
error-correcting quantum block code. We prove that {\em iff} a QECC results in
high fidelity for the case of no error the QECC can be recast into a form where
the encoder is the matrix inverse of the decoder.Comment: Resubmission with various corrections and expansions. See also
http://vesta.physics.ucla.edu/~smolin/ for related papers and information. 82
pages latex including 19 postscript figures included using psfig macro
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