Difficulty of distinguishing product states locally

Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is not enough for optimal decoding. For simple examples of pure product states, the gap in performance is known to be rather small when arbitrary local strategies are allowed. Here we restrict to local strategies readily achievable with current technology; those requiring neither a quantum memory nor joint operations. We show that, even for measurements on pure product states there can be a large gap between such strategies and theoretically optimal performance. Thus even in the absence of entanglement physically realizable local strategies can be far from optimal for extracting quantum information.Comment: 5 pages, 1 figur

Irreversibility in asymptotic manipulations of entanglement

We show that the process of entanglement distillation is irreversible by showing that the entanglement cost of a bound entangled state is finite. Such irreversibility remains even if extra pure entanglement is loaned to assist the distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states under pure entanglement catalytic LOCC adde

New classes of n-copy undistillable quantum states with negative partial transposition

The discovery of entangled quantum states from which one cannot distill pure entanglement constitutes a fundamental recent advance in the field of quantum information. Such bipartite bound-entangled (BE) quantum states \emph{could} fall into two distinct categories: (1) Inseparable states with positive partial transposition (PPT), and (2) States with negative partial transposition (NPT). While the existence of PPT BE states has been confirmed, \emph{only one} class of \emph{conjectured} NPT BE states has been discovered so far. We provide explicit constructions of a variety of multi-copy undistillable NPT states, and conjecture that they constitute families of NPT BE states. For example, we show that for every pure state of Schmidt rank greater than or equal to three, one can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance of such conjectured NPT BE states, we believe, considerably strengthens the notion that being NPT is only a necessary condition for a state to be distillable.Comment: Latex, 10 page

The Effect of Symmetry Lowering on the Dielectric Response of BaZrO3BaZrO_3

We use first-principles density functional theory calculations to investigate the dielectric response of BaZrO$_3$ perovskite. A previous study [Arkbarzadeh {\em et al.} Phys. Rev. B {\bf 72}, 205104 (2005)] reported a disagreement between experimental and theoretical low temperature dielectric constant $\epsilon$ for the high symmetry BaZrO$_3$ structure. We show that a fully relaxed 40-atom BaZrO$_3$ structure exhibits O$_6$ octahedral tilting, and $\epsilon$ that agrees with experiment. The change in $\epsilon$ from high-symmetry to low-symmetry structure is due to increased phonon frequencies as well as decreased mode effective charges.Comment: 4 pages, 2 figure

Separability and distillability of multiparticle quantum systems

We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to $N$--particle states.Comment: replaced with published version (Phys.Rev.Lett.), in parts rewritten and clarifie

Optimal Entanglement Enhancement for Mixed States

We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC and characterise the representatives with maximal entanglement of formation. We thus obtain a LQCC entanglement concentration protocol for a single given state (pure or mixed) of two qubits which is optimal in the sense that the protocol produces, with non-zero probability, a state of maximal possible entanglement of formation. This defines a new entanglement measure, the maximum extractable entanglement.Comment: Final version: to appear in Phys. Rev. Let

Moving Difference (MDIFF) Non-adiabatic Rapid Sweep (NARS) EPR of Copper(II)

Non-adiabatic rapid sweep (NARS) EPR spectroscopy has been introduced for application to nitroxide-labeled biological samples (Kittell et al., 2011). Displays are pure absorption, and are built up by acquiring data in spectral segments that are concatenated. In this paper we extend the method to frozen solutions of copper-imidazole, a square planar copper complex with four in-plane nitrogen ligands. Pure absorption spectra are created from concatenation of 170 5-gauss segments spanning 850 G at 1.9 GHz. These spectra, however, are not directly useful since nitrogen superhyperfine couplings are barely visible. Application of the moving difference (MDIFF) algorithm to the digitized NARS pure absorption spectrum is used to produce spectra that are analogous to the first harmonic EPR. The signal intensity is about four times higher than when using conventional 100 kHz field modulation, depending on line shape. MDIFF not only filters the spectrum, but also the noise, resulting in further improvement of the SNR for the same signal acquisition time. The MDIFF amplitude can be optimized retrospectively, different spectral regions can be examined at different amplitudes, and an amplitude can be used that is substantially greater than the upper limit of the field modulation amplitude of a conventional EPR spectrometer, which improves the signal-to-noise ratio of broad lines

Quantifying nonorthogonality

An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle density matrices using methods that are similar to recently introduced techniques for quantifying entanglement. Several interesting special cases are considered. It is pointed out that a measure of nonorthogonality can meaningfully be associated with a single mixed quantum state. It is then shown how nonorthogonality can be unlocked with classical information; this analysis reveals interesting inequalities and points to a number of connections between nonorthogonality and entanglement.Comment: Accepted for publication in Phys. Rev.

Entanglement sharing among qudits

Consider a system consisting of n d-dimensional quantum particles (qudits), and suppose that we want to optimize the entanglement between each pair. One can ask the following basic question regarding the sharing of entanglement: what is the largest possible value Emax(n,d) of the minimum entanglement between any two particles in the system? (Here we take the entanglement of formation as our measure of entanglement.) For n=3 and d=2, that is, for a system of three qubits, the answer is known: Emax(3,2) = 0.550. In this paper we consider first a system of d qudits and show that Emax(d,d) is greater than or equal to 1. We then consider a system of three particles, with three different values of d. Our results for the three-particle case suggest that as the dimension d increases, the particles can share a greater fraction of their entanglement capacity.Comment: 4 pages; v2 contains a new result for 3 qudits with d=

Entangled Rings

Consider a ring of N qubits in a translationally invariant quantum state. We ask to what extent each pair of nearest neighbors can be entangled. Under certain assumptions about the form of the state, we find a formula for the maximum possible nearest-neighbor entanglement. We then compare this maximum with the entanglement achieved by the ground state of an antiferromagnetic ring consisting of an even number of spin-1/2 particles. We find that, though the antiferromagnetic ground state does not maximize the nearest-neighbor entanglement relative to all other states, it does so relative to other states having zero z-component of spin.Comment: 19 pages, no figures; v2 includes new results; v3 corrects a numerical error for the case N=