# Publications

## Atom state evolution and collapse in ultracold gases during light scattering into a cavity

Laser Physics **21** (2011) 1486-1490

## A functional interpretation of continuous variable quantum discord

Optics InfoBase Conference Papers (2011) 1200-1202

We show that quantum discord can quantify the information advantage of a quantum processing over an optimal classical processing. We experimentally extract a lower bound on the quantum discord of a non-entangled continuous-variable quantum system. © 2011 AOS.

## Experimental demonstration of a unified framework for mixed-state geometric phases

EPL **94** (2011)

Geometric phases have been found in every major branch of physics and play an important role in mathematics and quantum computation. Here, we unify two proposed definitions of the geometric phase in mixed states - Uhlmann's phase and Sjöqvist's phase - in a new formalism based on interferometry and further provide an experimental demonstration in NMR. This is also the first experimental measurement of Uhlmann's geometric phase. © 2011 Europhysics Letters Association.

## Quantum Correlations in Mixed-State Metrology

Physical Review X **1** (2011) 1-9

We analyze the effects of quantum correlations, such as entanglement and discord, on the efficiency of phase estimation by studying four quantum circuits that can be readily implemented using NMR techniques. These circuits define a standard strategy of repeated single-qubit measurements, a classical strategy where only classical correlations are allowed, and two quantum strategies where nonclassical correlations are allowed. In addition to counting space (number of qubits) and time (number of gates) requirements, we introduce mixedness as a key constraint of the experiment.We compare the efficiency of the four strategies as a function of the mixedness parameter. We find that the quantum strategy gives ffiffiffiffi N p enhancement over the standard strategy for the same amount of mixedness. This result applies even for highly mixed states that have nonclassical correlations but no entanglement.

## Statistical mechanics of the cluster Ising model

Physical Review A - Atomic, Molecular, and Optical Physics **84** (2011)

We study a Hamiltonian system describing a three-spin-1/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class. © 2011 American Physical Society.

## Geometric local invariants and pure three-qubit states

Physical Review A - Atomic, Molecular, and Optical Physics **83** (2011)

We explore a geometric approach to generating local SU(2) and SL(2,C) invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or "gauge" invariant is associated with a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters, and the gauge invariant observable associated with a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link transformations between the qubits are defined by the correlations between them, and the gauge invariant observable, the local invariants associated with a particular closed path, are also given by a Wilson looplike construction. The link transformations share many of the properties of parallel transporters, although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three-qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way; however, the framework given here is applicable to generating local unitary invariants for mixed states composed of any number of d-level quantum systems. We give an operational interpretation of these invariants in terms of observables. © 2011 American Physical Society.

## Few-body bound states in dipolar gases and their detection

Phys. Rev. Lett. **107** (2011) 073201-

We consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intratube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to many tubes and layers, and outline the implications on many-body physics.

## The thermodynamic meaning of negative entropy.

Nature **474** (2011) 61-63

The heat generated by computations is not only an obstacle to circuit miniaturization but also a fundamental aspect of the relationship between information theory and thermodynamics. In principle, reversible operations may be performed at no energy cost; given that irreversible computations can always be decomposed into reversible operations followed by the erasure of data, the problem of calculating their energy cost is reduced to the study of erasure. Landauer's principle states that the erasure of data stored in a system has an inherent work cost and therefore dissipates heat. However, this consideration assumes that the information about the system to be erased is classical, and does not extend to the general case where an observer may have quantum information about the system to be erased, for instance by means of a quantum memory entangled with the system. Here we show that the standard formulation and implications of Landauer's principle are no longer valid in the presence of quantum information. Our main result is that the work cost of erasure is determined by the entropy of the system, conditioned on the quantum information an observer has about it. In other words, the more an observer knows about the system, the less it costs to erase it. This result gives a direct thermodynamic significance to conditional entropies, originally introduced in information theory. Furthermore, it provides new bounds on the heat generation of computations: because conditional entropies can become negative in the quantum case, an observer who is strongly correlated with a system may gain work while erasing it, thereby cooling the environment.

## Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate

Physical Review A - Atomic, Molecular, and Optical Physics **83** (2011)

We use entanglement to investigate the transition from vortex-liquid phase to vortex-lattice phase in a weakly interacting rotating Bose-Einstein condensate. For the torus geometry, the ground-state entanglement spectrum is analyzed to distinguish these two phases. The low-lying part of the ground-state entanglement spectrum, as well as the behavior of its lowest level, changes clearly when the transition occurs. For the sphere geometry, the entanglement gap in the conformal limit is also studied. We also show that the decrease in entanglement between particles can be regarded as a signal of the transition. © 2011 American Physical Society.

## Quantum Correlations in Biomolecules

22ND SOLVAY CONFERENCE ON CHEMISTRY: QUANTUM EFFECTS IN CHEMISTRY AND BIOLOGY **3** (2011)

## Discussions on Session 3A: Quantum dynamic theory

22ND SOLVAY CONFERENCE ON CHEMISTRY: QUANTUM EFFECTS IN CHEMISTRY AND BIOLOGY **3** (2011)

## Global asymmetry of many-qubit correlations: A lattice-gauge-theory approach

PHYSICAL REVIEW A **84** (2011) ARTN 032302

## Discussions on Session 3B: Quantum dynamic theory

22ND SOLVAY CONFERENCE ON CHEMISTRY: QUANTUM EFFECTS IN CHEMISTRY AND BIOLOGY **3** (2011)

## Generating topological order from a two-dimensional cluster state using a duality mapping

New Journal of Physics **13** (2011)

In this paper, we prove, extend and review possible mappings between the two-dimensional (2D) cluster state, Wen's model, the 2D Ising chain and Kitaev's toric code model. We introduce a 2D duality transformation to map the 2D lattice cluster state into the topologically ordered Wen model. Then, we investigate how this mapping could be achieved physically, which allows us to discuss the rate at which a topologically ordered system can be achieved. Next, using a lattice fermionization method, Wen's model is mapped into a series of 1D Ising interactions. Considering the boundary terms with this mapping then reveals how the Ising chains interact with one another. The duality of these models can be taken as a starting point to address questions as to how their gate operations in different quantum computational models can be related to each other. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## Quantum phase transition between cluster and antiferromagnetic states

EPL **95** (2011)

We study a Hamiltonian system describing a three-spin-1/2 cluster-like interaction competing with an Ising-like exchange. We show that the ground state in the cluster phase possesses symmetry protected topological order. A continuous quantum phase transition occurs as result of the competition between the cluster and Ising terms. At the critical point the Hamiltonian is self-dual. The geometric entanglement is also studied and used to investigate the quantum phase transition. Our findings in one dimension corroborate the analysis of the two-dimensional generalization of the system, indicating, at a mean-field level, the presence of a direct transition between an antiferromagnetic and a valence bond solid ground state. © 2011 EPLA.

## Sustained quantum coherence and entanglement in the avian compass.

Phys Rev Lett **106** (2011) 040503-

In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds have the ability to sense very subtle variations in Earth's magnetic field. Here we apply quantum information theory and the widely accepted "radical pair" model to analyze recent experimental observations of the avian compass. We find that superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best comparable man-made molecular systems. This conclusion is starkly at variance with the view that life is too "warm and wet" for such quantum phenomena to endure.