Complete Separability and Fourier representations of n-qubit states

Necessary conditions for separability are most easily expressed in the computational basis, while sufficient conditions are most conveniently expressed in the spin basis. We use the Hadamard matrix to define the relationship between these two bases and to emphasize its interpretation as a Fourier transform. We then prove a general sufficient condition for complete separability in terms of the spin coefficients and give necessary and sufficient conditions for the complete separability of a class of generalized Werner densities. As a further application of the theory, we give necessary and sufficient conditions for full separability for a particular set of $n$-qubit states whose densities all satisfy the Peres condition

What Good Can There Be In This Kind of Human? Spanish Justification for the Conquest of the Americas

The Spanish conquest of the Americas was one of the most brutal episodes in human history. Entire cultures of American natives were suppressed, murdered, raped, and enslaved by Spanish conquistadors on an incessant quest for precious metals and other material wealth. The devastation wrought upon the natives was so great that some Spaniards felt that what they were doing violated God\u27s will and was naturally and morally wrong, but they were vastly outnumbered. The majority saw it as their right, duty, and privilege to conquer and subject these millions of people to Spanish rule. Since they were trying to justify their case to sovereigns and a public that were thousands of miles away, they had to convey their reports regarding the natives in a favorable light. This often resulted in grossly exaggerated or even outright false reports regarding the behavior and customs of the natives. The conquistadors were eager to prove that what they were perpetrating on the natives was in fact completely justified and morally acceptable. As a result, the Spanish conquistadors dehumanized and demeaned the natives in their accounts of the conquest with the goal of making their actions seem justified and morally correct

It's Not a Matter of Time: Highlights From the 2011 Competency-Based Learning Summit

Outlines discussions about the potential and challenges of competency-based learning in transforming the current time-based system, including issues of accountability, equity, personalization, and aligning policy and practice. Includes case summaries

The Girl With The Tan Hair

I was the long desired baby sister with the tan hair. My brother, who was six years old at the time of my birth, had ordered me specially. Because he greatly admired the blond baby sister of one of his boy friends, he made numerous and serious appeals and accepted my arrival with the same enthusiasm as he had displayed when given his highly-prized, red tricycle. Although most people called me a towhead, Bob still considered me his little sister with the tan hair

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

The geometry of entanglement witnesses and local detection of entanglement

Let $H^{[ N]}=H^{[ d_{1}]}\otimes ... \otimes H^{[ d_{n}]}$ be a tensor product of Hilbert spaces and let $\tau_{0}$ be the closest separable state in the Hilbert-Schmidt norm to an entangled state $\rho_{0}$. Let $\tilde{\tau}_{0}$ denote the closest separable state to $\rho_{0}$ along the line segment from $I/N$ to $\rho_{0}$ where $I$ is the identity matrix. Following [pitrubmat] a witness $W_{0}$ detecting the entanglement of $\rho_{0}$ can be constructed in terms of $I, \tau_{0}$ and $\tilde{\tau}_{0}$. If representations of $\tau_{0}$ and $\tilde{\tau}_{0}$ as convex combinations of separable projections are known, then the entanglement of $\rho_{0}$ can be detected by local measurements. G\"{u}hne \textit{et. al.} in [bruss1] obtain the minimum number of measurement settings required for a class of two qubit states. We use our geometric approach to generalize their result to the corresponding two qudit case when $d$ is prime and obtain the minimum number of measurement settings. In those particular bipartite cases, $\tau_{0}=\tilde{\tau}_{0}$. We illustrate our general approach with a two parameter family of three qubit bound entangled states for which $\tau_{0} \neq \tilde{\tau}_{0}$ and we show our approach works for $n$ qubits. In [pitt] we elaborated on the role of a ``far face'' of the separable states relative to a bound entangled state $\rho_{0}$ constructed from an orthogonal unextendible product base. In this paper the geometric approach leads to an entanglement witness expressible in terms of a constant times $I$ and a separable density $\mu_{0}$ on the far face from $\rho_{0}$. Up to a normalization this coincides with the witness obtained in [bruss1] for the particular example analyzed there

A Point of View

For many years I had the distorted idea that a large back yard was a luxury to be desired since ours was comparatively small. I had gazed with envy at spacious, green lawns, edged with even, neatly trimmed hedges, with perhaps a row of rustling popular trees at one end, and carefully tended rock gardens at the other, rendering it a scene of symetry and color; yards with rose-covered trellises or graceful bird baths