On the communication cost of entanglement transformations

We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462, 1999], requires a number of bits to be exchanged which is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of ``embezzling entanglement'' [W. van Dam and P. Hayden, quant-ph/0201041].Comment: 9 pages, 1 figure. Added a reference and some further explanations. In v3 some arguments are given in more detai

The private capacity of quantum channels is not additive

Recently there has been considerable activity on the subject of additivity of various quantum channel capacities. Here, we construct a family of channels with sharply bounded classical, hence private capacity. On the other hand, their quantum capacity when combined with a zero private (and zero quantum) capacity erasure channel, becomes larger than the previous classical capacity. As a consequence, we can conclude for the first time that the classical private capacity is non-additive. In fact, in our construction even the quantum capacity of the tensor product of two channels can be greater than the sum of their individual classical private capacities. We show that this violation occurs quite generically: every channel can be embedded into our construction, and a violation occurs whenever the given channel has larger entanglement assisted quantum capacity than (unassisted) classical capacity.Comment: 4+4 pages, 2 eps figures. V2 has title and abstract changed; its new structure reflects the final version of a main paper plus appendices containing mathematical detail

A novel method for unambiguous ion identification in mixed ion beams extracted from an EBIT

A novel technique to identify small fluxes of mixed highly charged ion beams extracted from an Electron Beam Ion Trap (EBIT) is presented and practically demonstrated. The method exploits projectile charge state dependent potential emission of electrons as induced by ion impact on a metal surface to separate ions with identical or very similar mass-to-charge ratio.Comment: 8 pages, 5 figure

Composite Accretion Disk and White Dwarf Photosphere Analyses of the FUSE and HST Observations of EY Cygni

We explore the origin of FUSE and HST STIS far UV spectra of the dwarf nova, EY Cyg, during its quiescence using \emph{combined} high gravity photosphere and accretion disk models as well as model accretion belts. The best-fitting single temperature white dwarf model to the FUSE plus HST STIS spectrum of EY Cygni has T$_{eff} = 24,000$K, log $g = 9.0$, with an Si abundance of 0.1 x solar and C abundance of 0.2 x solar but the distance is only 301 pc. The best-fitting composite model consists of white dwarf with T$_{eff} = 22,000$K, log $g = 9$, plus an accretion belt with T$_{belt} = 36,000$K covering 27% of the white dwarf surface with V$_{belt} sin i = 2000$ km/s. The accretion belt contributes 63% of the FUV light and the cooler white dwarf latitudes contribute 37%. This fit yields a distance of 351 pc which is within 100 pc of our adopted distance of 450 pc. EY Cyg has very weak C {\sc iv} emission and very strong N {\sc v} emission, which is atypical of the majority of dwarf novae in quiescence. We also conducted a morphological study of the surroundings of EY Cyg using direct imaging in narrow nebular filters from ground-based telescopes. We report the possible detection of nebular material^M associated with EY Cygni. Possible origins of the apparently large N {\scv}/C {\sc iv} emission ratio are discussed in the context of nova explosions, contamination of the secondary star and accretion of nova abundance-enriched matter back to the white dwarf via the accretion disk or as a descendant of a precursor binary that survived thermal timescale mass transfer. The scenario involving pollution of the secondary by past novae may be supported by the possible presence of a nova remnant-like nebula around EY Cyg.Comment: To appear in AJ, Oct. 2004. 5 figures, including 2 color ones (2D pictures

Trading quantum for classical resources in quantum data compression

We study the visible compression of a source E of pure quantum signal states, or, more formally, the minimal resources per signal required to represent arbitrarily long strings of signals with arbitrarily high fidelity, when the compressor is given the identity of the input state sequence as classical information. According to the quantum source coding theorem, the optimal quantum rate is the von Neumann entropy S(E) qubits per signal. We develop a refinement of this theorem in order to analyze the situation in which the states are coded into classical and quantum bits that are quantified separately. This leads to a trade--off curve Q(R), where Q(R) qubits per signal is the optimal quantum rate for a given classical rate of R bits per signal. Our main result is an explicit characterization of this trade--off function by a simple formula in terms of only single signal, perfect fidelity encodings of the source. We give a thorough discussion of many further mathematical properties of our formula, including an analysis of its behavior for group covariant sources and a generalization to sources with continuously parameterized states. We also show that our result leads to a number of corollaries characterizing the trade--off between information gain and state disturbance for quantum sources. In addition, we indicate how our techniques also provide a solution to the so--called remote state preparation problem. Finally, we develop a probability--free version of our main result which may be interpreted as an answer to the question: ``How many classical bits does a qubit cost?'' This theorem provides a type of dual to Holevo's theorem, insofar as the latter characterizes the cost of coding classical bits into qubits.Comment: 51 pages, 7 figure

Photo-labile BODIPY protecting groups for glycan synthesis

Protective groups that can be selectively removed under mild conditions are an essential aspect of carbohydrate chemistry. Groups that can be selectively removed by visible light are particularly attractive because carbohydrates are transparent to visible light. Here, different BODIPY protecting groups were explored for their utility during glycan synthesis. A BODIPY group bearing a boron difluoride unit is stable during glycosylations but can be cleaved with green light as illustrated by the assembly of a trisaccharide

Existence and stability of singular patterns in a Ginzburg–Landau equation coupled with a mean field

We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg–Landau equation and a mean field equation. We prove the existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency conditions. In the case of spike patterns we prove stability for sufficiently large spatial periods by first showing that the eigenvalues do not tend to zero as the period goes to infinity and then passing in the limit to a nonlocal eigenvalue problem which can be studied explicitly. For the two other patterns we show instability by using the variational characterization of eigenvalues

On the dimension of subspaces with bounded Schmidt rank

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al., which show that in large d x d--dimensional systems there exist random subspaces of dimension almost d^2, all of whose states have entropy of entanglement at least log d - O(1). It is also related to results due to Parthasarathy on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions dA and dB, and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using random subspace techniques. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r.Comment: 4 pages, REVTeX4 forma