A separability criterion for density operators

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.Comment: REVTeX, 5 page

Probabilistic Quantum Memories

Typical address-oriented computer memories cannot recognize incomplete or noisy information. Associative (content-addressable) memories solve this problem but suffer from severe capacity shortages. I propose a model of a quantum memory that solves both problems. The storage capacity is exponential in the number of qbits and thus optimal. The retrieval mechanism for incomplete or noisy inputs is probabilistic, with postselection of the measurement result. The output is determined by a probability distribution on the memory which is peaked around the stored patterns closest in Hamming distance to the input.Comment: Revised version to appear in Phys. Rev. Let

Geometrical approach to mutually unbiased bases

We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.Comment: 10 pages. Some typos in the journal version have been correcte

Mutually unbiased bases and discrete Wigner functions

Mutually unbiased bases and discrete Wigner functions are closely, but not uniquely related. Such a connection becomes more interesting when the Hilbert space has a dimension that is a power of a prime $N=d^n$, which describes a composite system of $n$ qudits. Hence, entanglement naturally enters the picture. Although our results are general, we concentrate on the simplest nontrivial example of dimension $N=8=2^3$. It is shown that the number of fundamentally different Wigner functions is severely limited if one simultaneously imposes translational covariance and that the generating operators consist of rotations around two orthogonal axes, acting on the individual qubits only.Comment: 9 pages, 6 tables, 6 figures. Accepted for publication in J. Opt. Soc. Am. B, special issue on Optical Quantum Information Scienc

Generalized reduction criterion for separability of quantum states

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.Comment: 17 pages, 2 figure

Excision of a strong Markov process

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47651/1/440_2004_Article_BF00532853.pd

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Quantum Measurement of a Single Spin using Magnetic Resonance Force Microscopy

Single-spin detection is one of the important challenges facing the development of several new technologies, e.g. single-spin transistors and solid-state quantum computation. Magnetic resonance force microscopy with a cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by a single spin, is a promising technique to solve this problem. We have studied the quantum dynamics of a single spin interacting with a quasiclassical cantilever. It was found that in a similar fashion to the Stern-Gerlach interferometer the quantum dynamics generates a quantum superposition of two quasiclassical trajectories of the cantilever which are related to the two spin projections on the direction of the effective magnetic field in the rotating reference frame. Our results show that quantum jumps will not prevent a single-spin measurement if the coupling between the cantilever vibrations and the spin is small in comparison with the amplitude of the radio-frequency external field.Comment: 16 pages RevTeX including 4 figure

Evolving faces from principal components

A system that uses an underlying genetic algorithm to evolve faces in response to user selection is described. The descriptions of faces used by the system are derived from a statistical analysis of a set of faces. The faces used for generation are transformed to an average shape by defining locations around each face and morphing. The shape-free images and shape vectors are then separately subjected to principal components analysis. Novel faces are generated by recombining the image components ("eigenfaces") and then morphing their shape according to the principal components of the shape vectors ("eigenshapes"). The prototype system indicates that such statistical analysis of a set of faces can produce plausible, randomly generated photographic images

Target experimental area and systems of the U.S. National Ignition Facility

One of the major goals of the US National Ignition Facility is the demonstration of laser driven fusion ignition and burn of targets by inertial confinement and provide capability for a wide variety of high energy density physics experiments. The NIF target area houses the optical systems required to focus the 192 beamlets to a target precisely positioned at the center of the 10 meter diameter, 10-cm thick aluminum target chamber. The chamber serves as mounting surface for the 48 final optics assemblies, the target alignment and positioning equipment, and the target diagnostics. The internal surfaces of the chamber are protected by louvered steel beam dumps. The target area also provides the necessary shielding against target emission and environmental protection equipment. Despite its complexity, the design provides the flexibility to accommodate the needs of the various NIF user groups, such as direct and indirect drive irradiation geometries, modular final optics design, capability to handle cryogenic targets, and easily re-configurable diagnostic instruments. Efficient target area operations are ensured by using line-replaceable designs for systems requiring frequent inspection, maintenance and reconfiguration, such as the final optics, debris shields, phase plates and the diagnostic instruments. A precision diagnostic instrument manipulator (DIMS) allows fast removal and precise repositioning of diagnostic instruments. In addition the authors describe several activities to enhance the target chamber availability, such as the target debris mitigation, the use of standard experimental configurations and the development of smart shot operations planning tools