Probabilistic quantum multimeters

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states, then the universal multimeters for a special choice of program. In both cases we start with deterministic but erroneous devices and then proceed to devices that never make a mistake but from time to time they give an inconclusive result. These multimeters are optimized (for a given type of a program) with respect to the minimum probability of inconclusive result. This concept is further generalized to the multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.Comment: 12 pages, 3 figure

CP^n, or, entanglement illustrated

We show that many topological and geometrical properties of complex projective space can be understood just by looking at a suitably constructed picture. The idea is to view CP^n as a set of flat tori parametrized by the positive octant of a round sphere. We pay particular attention to submanifolds of constant entanglement in CP^3 and give a few new results concerning them.Comment: 28 pages, 9 figure

Structural stability and local electronic properties of some EC synthesized magnetite nanopowders

Structural and electronic properties, oxidation and aging effect of electrochemically (EC) synthesized magnetite nanopowders (NPs) are studied by means of X–ray diffraction (XRD), X–ray absorption fine structure (XAFS) and X–ray magnetic circular dichroism (XMCD). The obtained results enabled to get a direct insight into the structure and electronic properties of Fe immediate surrounding and to elucidate the influence of preparation conditions on stoichiometry of NPs and their stability in ambient conditions. All investigated NPs are produced as non–stoichiometric Fe$_{3−δ}$O$_4$ oxide phases, with the lattice constant and the Fe$^{2+}$/Fe$^{3+}$ ratio both in–between the values for bulk maghemite and magnetite. NPs synthesized under smaller current density (J = 200 mA/dm$^2$) are more magnetite–alike, whereas larger current density (J = 1000 mA/dm$^2$) has led to formation of NPs closer to maghemite. Oxidation of magnetite–like NPs is slower, although in the course of time particles agglomerate and oxide penetrates into the core. Maghemite–like NPs oxidize much faster and the oxide layer which is confined close to the particles' surface protects the core from further oxidation. In all NPs the fist coordination around Fe is pretty stable against both temperature and oxidation process. The temperature change from 293 K to 20 K considerably affects the second coordination around Fe, which is most likely a consequence of the Verwey transition present in all investigated samples

Experimental Demonstration of Optimal Unambiguous State Discrimination

We present the first full demonstration of unambiguous state discrimination between non-orthogonal quantum states. Using a novel free space interferometer we have realised the optimum quantum measurement scheme for two non-orthogonal states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have for the first time gained access to all three possible outcomes of this measurement. All aspects of this generalised measurement scheme, including its superiority over a standard von Neumann measurement, have been demonstrated within 1.5% of the IDP predictions

Distinguishing two-qubit states using local measurements and restricted classical communication

The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties, Alice and Bob, are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure has been shown to be the same as if the particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party's measurement depends on the result of the other party's. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of these procedures, in particular to secret sharing, are discussed.Comment: 18 pages, two figure

Maximal Entanglement, Collective Coordinates and Tracking the King

Maximal entangled states (MES) provide a basis to two d-dimensional particles Hilbert space, d=prime $\ne 2$. The MES forming this basis are product states in the collective, center of mass and relative, coordinates. These states are associated (underpinned) with lines of finite geometry whose constituent points are associated with product states carrying Mutual Unbiased Bases (MUB) labels. This representation is shown to be convenient for the study of the Mean King Problem and a variant thereof, termed Tracking the King which proves to be a novel quantum communication channel. The main topics, notions used are reviewed in an attempt to have the paper self contained.Comment: 8. arXiv admin note: substantial text overlap with arXiv:1206.3884, arXiv:1206.035

Redox-inactive ions control the redox-activity of molecular vanadium oxides

Polyoxometalates are key materials for energy conversion and storage due to their unique chemical tunability and electrochemical reactivity. Herein, we report that functionalization of molecular vanadium oxides, polyoxovanadates, with redox-inert Ca$^{2+}$ cations leads to a significant increase in their electron storage capabilities. The electrochemical performance of the Ca$^{2+}$-functionalized dodecavanadate [Ca$_{2}$V$_{12}$O$_{32}$Cl(DMF) $_{3}$]$^{2-}$ (={Ca$_{2}$V$_{12}$}) was thus compared with that of the precursor compound (H$_{2}$NMe$_{2}$)$_{2}$ [V$_{12}$O$_{32}$Cl] $^{3-}$ (={V$_{12}$}). {Ca$_{2}$V$_{12}$} can store up to five electrons per cluster, while {V12} only shows one reversible redox transition. In initial studies, we demonstrated that {Ca$_{2}$V$_{12}$} can be used as an active material in lithium-ion cathodes. Our results show how redox-inert cations can be used as structural and electrostatic stabilizers, leading to major changes in the redox-chemistry of polyoxovanadates

The problem of mutually unbiased bases in dimension 6

We outline a discretization approach to determine the maximal number of mutually unbiased bases in dimension 6. We describe the basic ideas and introduce the most important definitions to tackle this famous open problem which has been open for the last 10 years. Some preliminary results are also listed