Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a ``memory'' of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution not only depends on the geometry of the path of the system alone but also on a constrained bi-local unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires uni-local transformations and is therefore essentially a property of the system alone.Comment: minor changes, journal reference adde

Tangles of superpositions and the convex-roof extension

We discuss aspects of the convex-roof extension of multipartite entanglement measures, that is, SL(2,\CC) invariant tangles. We highlight two key concepts that contain valuable information about the tangle of a density matrix: the {\em zero-polytope} is a convex set of density matrices with vanishing tangle whereas the {\em convex characteristic curve} readily provides a non-trivial lower bound for the convex roof and serves as a tool for constructing the convex roof outside the zero-polytope. Both concepts are derived from the tangle for superpositions of the eigenstates of the density matrix. We illustrate their application by considering examples of density matrices for two-qubit and three-qubit states of rank 2, thereby pointing out both the power and the limitations of the concepts.Comment: 7 pages, 5 figures, revtex

Deferred Prosecution and Non-Prosecution Agreements and the Erosion of Corporate Criminal Liability

On April 5, 2010, a massive explosion killed twenty-nine miners at Massey Energy's Upper Big Branch mine near Montcoal, West Virginia. Following the explosion, President Barack Obama vowed that the U.S. Department of Labor would conduct "the most thorough and comprehensive investigation possible" and work with the U.S. Department of Justice ("Justice Department" or the "Department") to address any criminal violations. Later in the month, the President and Vice President flew to West Virginia to eulogize the victims and comfort their families. It was the nation's worst coal mining disaster in forty years. The tragic loss of life at the Upper Big Branch mine was not an accident. After a twenty-month investigation, the Mine Safety and Health Administration ("MSHA") determined that the workers died because of a methane and coal dust explosion at the Upper Big Branch mine that was "entirely preventable." The MSHA identified over 300 violations of the Mine Safety and Health Act at the Upper Big Branch mine, including nine flagrant violations that contributed to the explosion. Without any of the hedging often found in safety investigations, MSHA concluded that Massey's "unlawful policies and practices... were the root cause" of the Upper Big Branch mine tragedy.http://deepblue.lib.umich.edu/bitstream/2027.42/107452/1/72MdLRev.pd

Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance

The role of mixed state entanglement in liquid-state nuclear magnetic resonance (NMR) quantum computation is not yet well-understood. In particular, despite the success of quantum information processing with NMR, recent work has shown that quantum states used in most of those experiments were not entangled. This is because these states, derived by unitary transforms from the thermal equilibrium state, were too close to the maximally mixed state. We are thus motivated to determine whether a given NMR state is entanglable - that is, does there exist a unitary transform that entangles the state? The boundary between entanglable and nonentanglable thermal states is a function of the spin system size $N$ and its temperature $T$. We provide new bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N \sim T$, giving a lower bound requiring at least $N \sim 22,000$ proton spins to realize an entanglable thermal state at typical laboratory NMR magnetic fields. These bounds are tighter than known bounds on the entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K

Concurrence of mixed bipartite quantum states in arbitrary dimensions

We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed entangled states with positive partial transpose.Comment: accepted py PR