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

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

Hardy-type Inequalities Via Auxiliary Sequences

We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.Comment: 10 page

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