Optimal quantum teleportation with an arbitrary pure state

We derive the maximum fidelity attainable for teleportation using a shared pair of d-level systems in an arbitrary pure state. This derivation provides a complete set of necessary and sufficient conditions for optimal teleportation protocols. We also discuss the information on the teleported particle which is revealed in course of the protocol using a non-maximally entangled state.Comment: 10 pages, REVTe

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure

Supercatalysis

We show that entanglement-assisted transformations of bipartite entangled states can be more efficient than catalysis [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)}, i.e., given two incomparable bipartite states not only can the transformation be enabled by performing collective operations with an auxiliary entangled state, but the entanglement of the auxiliary state itself can be enhanced. We refer to this phenomenon as supercatalysis. We provide results on the properties of supercatalysis and its relationship with catalysis. In particular, we obtain a useful necessary and sufficient condition for catalysis, provide several sufficient conditions for supercatalysis and study the extent to which entanglement of the auxiliary state can be enhanced via supercatalysis.Comment: Latex, 5 page

A quantization procedure based on completely positive maps and Markov operators

We describe $\omega$-limit sets of completely positive (CP) maps over finite-dimensional spaces. In such sets and in its corresponding convex hulls, CP maps present isometric behavior and the states contained in it commute with each other. Motivated by these facts, we describe a quantization procedure based on CP maps which are induced by Markov (transfer) operators. Classical dynamics are described by an action over essentially bounded functions. A non-expansive linear map, which depends on a choice of a probability measure, is the centerpiece connecting phenomena over function and matrix spaces

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

Classical Open String Models in 4-Dim Minkowski Spacetime

Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that can depend on second order derivatives of worldsheet coordinates. A revised interpretation of the variational problem for such theories is given. We derive a general form of a boundary term that can be added to the open string action to control edge conditions and modify conservation laws. An extended boundary problem for minimal surfaces is examined. Following the treatment of this model in the geometric approach, we obtain that classical open string states correspond to solutions of a complex Liouville equation. In contrast to the Nambu-Goto case, the Liouville potential is finite and constant at worldsheet boundaries. The phase part of the potential defines topological sectors of solutions.Comment: 25 pages, LaTeX, preprint TPJU-28-93 (the previous version was truncated by ftp...

Ordering states with entanglement measures

We demonstrate that all good asymptotic entanglement measures are either identical or place a different ordering on the set of all quantum states.Comment: 6 pages, minor changes, references updated, all conclusions unchanged, now accepted for publicatio

Mucoadhesive electrospun patch delivery of lidocaine to the oral mucosa and investigation of spatial distribution in tissue using MALDI-mass spectrometry imaging

Many oral mucosal conditions cause considerable and prolonged pain that to date has been difficult to alleviate via topical delivery, and the use of injection causes many patients dental anxiety and needle-prick pain. Therefore, developing a non-injectable drug delivery system as an alternative administration procedure may vastly improve the health and wellbeing of these patients. Recent advances in the development of mucoadhesive electrospun patches for the direct delivery of therapeutics to the oral mucosa offer a potential solution, but as yet, the release of local anaesthetics from this system and their uptake by oral tissue has not been demonstrated. Here, we demonstrate the fabrication of lidocaine-loaded electrospun fibre patches, drug release, and subsequent uptake and permeation through porcine buccal mucosa. Lidocaine HCl and lidocaine base were incorporated into the electrospun patches to evaluate the difference in drug permeation for the two drug compositions. Lidocaine released from the lidocaine HCl-containing electrospun patches was significantly quicker than from the lidocaine base patches, with double the amount of drug released from the lidocaine HCl patches in the first 15 minutes (0.16 ± 0.04 mg) compared to from the lidocaine base patches (0.07 ± 0.01 mg). The permeation of lidocaine from the lidocaine HCl electrospun patches through ex vivo porcine buccal mucosa was also detected in 15 minutes, whereas permeation of lidocaine from the lidocaine base patch was not detected. Matrix-assisted laser desorption ionisation – mass spectrometry imaging (MALDI-MSI) was used to investigate localisation of lidocaine within oral tissue. Lidocaine in solution as well as from the mucoadhesive patch penetrated into buccal mucosal tissue in a time-dependent manner and was detectable in the lamina propria after only 15 minutes. Moreover, the lidocaine released from lidocaine HCl electrospun patches retained biological activity, inhibiting veratridine-mediated opening of voltage-gated sodium channels in SH-SY5Y neuroblastoma cells. These data suggest that a mucoadhesive electrospun patch may be used as a vehicle for rapid uptake and sustained anaesthetic drug delivery and may reduce the need for injection

Continuity of the von Neumann entropy

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and to obtain several new conditions. The method is based on a particular approximation of the von Neumann entropy by an increasing sequence of concave continuous unitary invariant functions defined using decompositions into finite rank operators. The existence of this approximation is a corollary of a general property of the set of quantum states as a convex topological space called the strong stability property. This is considered in the first part of the paper.Comment: 42 pages, the minor changes have been made, the new applications of the continuity condition have been added. To appear in Commun. Math. Phy