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

Uhlmann Rejoinder to: Taubman’s “Letter to the Editor”

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146973/1/jgc40419.pd

Two qubits can be entangled in two distinct temperature regions

We have found that for a wide range of two-qubit Hamiltonians the canonical-ensemble thermal state is entangled in two distinct temperature regions. In most cases the ground state is entangled; however we have also found an example where the ground state is separable and there are still two regions. This demonstrates that the qualitative behavior of entanglement with temperature can be much more complicated than might otherwise have been expected; it is not simply determined by the entanglement of the ground state, even for the simple case of two qubits. Furthermore, we prove a finite bound on the number of possible entangled regions for two qubits, thus showing that arbitrarily many transitions from entanglement to separability are not possible. We also provide an elementary proof that the spectrum of the thermal state at a lower temperature majorizes that at a higher temperature, for any Hamiltonian, and use this result to show that only one entangled region is possible for the special case of Hamiltonians without magnetic fields.Comment: 6 pages, 4 figures, many new result

National Society of Genetic Counselors Natalie Weissburger Paul Lifetime Achievement Award Address: The Power of Connecting

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147102/1/jgc40007.pd

Fidelity and Concurrence of conjugated states

We prove some new properties of fidelity (transition probability) and concurrence, the latter defined by straightforward extension of Wootters notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operators. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two- and tripartite systems illustrate the general theorem.Comment: 10 pages, RevTex, Correction: Enlarged, reorganized version. More explanation

Response to Robert G. Resta Commentary (Unprepared, Understaffed, and Unplanned: Thoughts on the Practical Implications of Discovering New Breast and Ovarian Cancer Causing Genes)

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147069/1/jgc40524.pd

O(N) symmetry-breaking quantum quench: Topological defects versus quasiparticles

We present an analytical derivation of the winding number counting topological defects created by an O(N) symmetry-breaking quantum quench in N spatial dimensions. Our approach is universal in the sense that we do not employ any approximations apart from the large-$N$ limit. The final result is nonperturbative in N, i.e., it cannot be obtained by %the usual an expansion in 1/N, and we obtain far less topological defects than quasiparticle excitations, in sharp distinction to previous, low-dimensional investigations.Comment: 6 pages of RevTex4-1, 1 figure; to be published in Physical Review

A simple operational interpretation of the fidelity

This note presents a corollary to Uhlmann's theorem which provides a simple operational interpretation for the fidelity of mixed states.Comment: 1 pag

Probability distributions consistent with a mixed state

A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, \rho = \sum_i p_i |\psi_i\ra \la \psi_i|. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a decomposition, for a fixed density matrix $\rho$. Several illustrative applications of this result to quantum mechanics and quantum information theory are given.Comment: 6 pages, submitted to Physical Review

Crystallization, flow and thermal histories of lunar and terrestrial compositions

Contents: a kinetic treatment of glass formation; effects of nucleating heterogeneities on glass formation; glass formation under continuous cooling conditions; crystallization statistics; kinetics of crystal nucleation; diffusion controlled crystal growth; crystallization of lunar compositions; crystallization between solidus and liquidus; crystallization on reheating a glass; temperature distributions during crystallization; crystallization of anorthite and anorthite-albite compositions; effect of oxidation state on viscosity; diffusive creep and viscous flow; high temperature flow behavior of glass-forming liquids, a free volume interpretation; viscous flow behavior of lunar compositions; thermal history of orange soil material; breccias formation by viscous sintering; viscous sintering; thermal histories of breccias; solute partitioning and thermal history of lunar rocks; heat flow in impact melts; and thermal histories of olivines