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

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

EIN RECHNERPROGRAMM ZUR BESTlMMUNG DER ZUGFOLGE BEIM ABWEICHEN VON DER STRECKENFAHRORDNUNG

Ursachen des Abweichens von der Streckenführung. Zielfunktion für das Rechenprogramm für das Ahweichen von der Streckenfahrordnung. Rolle der Einordnung der Züge in der Prioritätsgattung. Rechentechnische Realisation des Programmes am Bürocomputer A 5120, Programmiersprache BASIC

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

Prosecuting Worker Endangerment: The Need for Stronger Criminal Penalties for Violations of the Occupational Safety and Health Act

A recent spate of construction deaths in New York City, similar incidents in Las Vegas, and scores of fatalities in recent years at mines and industrial facilities across the country have highlighted the need for greater commitment to worker safety in the United States and stronger penalties for violators of the worker safety laws. Approximately 6,000 workers are killed on the job each year1—and thousands more suffer grievous injuries—yet penalties for worker safety violations remain appallingly small, and criminal prosecutions are almost non-existent. In recent years, most of the criminal prosecutions for worker safety violations have been brought by the Justice Department’s Environmental Crimes Section, which began a worker endangerment initiative in 2005 to highlight the fact that environmental crimes frequently place America’s workers at risk of death or serious bodily injury, and to prosecute companies that systematically violate both the environmental laws and the worker safety laws

The Pendulum Swings: Reconsidering Corporate Criminal Prosecution

Corporate crime continues to occur at an alarming rate, yet disagreement persists among scholars and practitioners about the role of corporate criminal prosecution. Some argue that corporations should face criminal prosecution for their misconduct, while others would reserve criminal prosecution for individual corporate officials. Perhaps as a result of this conflict, there has been a dramatic increase over the last decade in the use of deferred prosecution and non-prosecution agreements for some corporate crimes, even as the government continues to bring criminal charges for other corporate crimes. To move beyond our erratic approach to corporate crime, we need a better understanding of what is accomplished by the criminal prosecution of corporations, a construct that considers retributive and utilitarian theories but also takes into account the expressive function of criminal law and the societal need for condemnation, accountability, and justice when crime occurs. In this article, I provide a justification for corporate criminal prosecution that identifies the moral content of corporate crime, considers the deterrent value of corporate prosecution, and explains why the expressive value of the criminal law is indispensable in the corporate context. Corporate wrongdoing has pernicious effects on our communities, the economy, and the environment, which warrant the condemnation the criminal law provides. Criminal prosecution of corporations upholds the rule of law, validates the choices of law-abiding companies, and promotes accountability. Together those values contribute to our sense that justice has been done when crime occurs, which enhances trust in the legal system, provides the opportunity for societal catharsis, and allows us to move forward in the aftermath of criminal activity. When corporations face no consequences for their criminal behavior, we minimize their lawlessness, and increase cynicism about the outsized influence of corporations