211,240 research outputs found
Basic limitations for entanglement catalysis
In this paper we summarize the necessary condition for incomparable states
which can be catalyzed under entanglement-assisted LQCC (ELQCC). When we apply
an extended condition for entanglement transformation to entanglement-assisted
local manipulation we obtain a fundamental limit for entanglement catalysts.
Some relative questions are also discussed.Comment: 4 pages, revtex, no figure
Hardy-type Inequalities Via Auxiliary Sequences
We prove some Hardy-type inequalities via an approach that involves
constructing auxiliary sequences.Comment: 10 page
Quantum cryptography with polarizing interferometers
Cryptographic scheme proposed by Bennett, Brassard, and Mermin [Phys. Rev.
Lett. {\bf 68}, 557 (1992)] is reformulated in a version involving two
polarizing Mach-Zehnder interferometers. Such a form, although physically
equivalent to the original one, makes its security explicit, suggestive and
easy to explain to non-experts.Comment: revtex, 4 pages, 1 ps figur
Szego limit theorem for operators with discontinuous symbols and applications to entanglement entropy
The main result in this paper is a one term Szego type asymptotic formula
with a sharp remainder estimate for a class of integral operators of the
pseudodifferential type with symbols which are allowed to be non-smooth or
discontinuous in both position and momentum. The simplest example of such
symbol is the product of the characteristic functions of two compact sets, one
in real space and the other in momentum space. The results of this paper are
used in a study of the violation of the area entropy law for free fermions in
[18]. This work also provides evidence towards a conjecture due to Harold
Widom.Comment: 18 pages, major revision, to appear in Int. Math. Res. No
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
Dynamics of the entanglement rate in the presence of decoherence
The dynamics of the entanglement rate are investigated in this paper for
pairwise interaction and two special sets of initial states. The results show
that for the given interaction and the decoherence scheme, the competitions
between decohering and entangling lead to two different results--some initial
states may be used to prepare entanglement while the others do not. A criterion
on decohering and entangling is also presented and discussed.Comment: 5 pages, 2 figure
A Hausdorff-Young theorem for rearrangement-invariant spaces
The classical Hausdorff-Young theorem is extended to the setting of rearrangement-invariant spaces. More precisely, if 1 <_ p <_ 2, p[-1] + q[-1] = 1, and if X is a rearrangement-invariant space on the circle T with indices equal to p[-1], it is shown that there is a rearrangement-invariant space X on the integers Z with indices equal to q[-1] such that the Fourier transform is a bounded linear operator from X into X. Conversely, for any rearrangement-invariant space Y on Z with indices equal to q[-1], 2 < q <__ oo, there is a rearrangement-invariant space Y on T with indices equal to p[-1] such that J is bounded from Y into Y. Analogous results for other groups are indicated and examples are discussed when X is L[p] or a Lorentz space L[pr]
Resilience in the face of adversity
With the third anniversary of 9/11 just passed and the threat of terrorist attacks still ever-present, reflection both personally and professionally has become a greater part of our lives. In a dynamic marketing environment, now more than ever, it is important to value the personal characteristics that makes us rise above a crisis and forge new pathways. This reminds me of an outstanding conference presentation I heard at the Academy of Management annual conference two years ago. Dr Steven Freeman, of the University of Pennsylvania, won a prestigious Best Paper award for his presentation, which outlined how an investment bank located in the twin towers not only survived the crisis but increased its market share
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