# Publications

## An information-theoretic equality implying the Jarzynski relation

Journal of Physics A: Mathematical and Theoretical **45** (2012)

We derive a general informationtheoretic equality for a system undergoing two projective measurements separated by a general temporal evolution. The equality implies the non-negativity of the mutual information between the measurement outcomes of the earlier and later projective measurements. We show that it also contains the Jarzynski relation between the average exponential of the thermodynamical work and the exponential of the difference between the initial and final free energy. Our result elucidates the informationtheoretic underpinning of thermodynamics and explains why the Jarzynski relation holds identically both quantumly as well as classically. © 2012 IOP Publishing Ltd.

## The classical-quantum boundary for correlations: Discord and related measures

Reviews of Modern Physics **84** (2012)

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are among the more actively studied topics of quantum-information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here different notions of classical and quantum correlations quantified by quantum discord and other related measures are reviewed. In the first half, the mathematical properties of the measures of quantum correlations are reviewed, related to each other, and the classical-quantum division that is common among them is discussed. In the second half, it is shown that the measures identify and quantify the deviation from classicality in various quantum-information- processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. It is shown that in many cases quantum correlations indicate an advantage of quantum methods over classical ones. © 2012 American Physical Society.

## Unifying Typical Entanglement and Coin Tossing: On Randomization in Probabilistic Theories

Communications in Mathematical Physics **316** (2012) 441-487

It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quantum subspaces. The formula is exact and simple, only containing the number of degrees of freedom and the information capacity of the respective systems. It allows us to generalize statistical physics arguments in a way which depends only on coarse properties of the underlying theory. The proof of the formula generalizes several randomization notions to general probabilistic theories. This includes a generalization of purity, contributing to the recent effort of finding appropriate generalized entropy measures. © 2012 Springer-Verlag Berlin Heidelberg.

## Geometric-phase backaction in a mesoscopic qubit-oscillator system

Physical Review A - Atomic, Molecular, and Optical Physics **85** (2012)

We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro- and nanomechanical devices coupled to an effective two-level system. © 2012 American Physical Society.

## Topological order in 1D Cluster state protected by symmetry

Quantum Information Processing **11** (2012) 1961-1968

We demonstrate how to construct the Z2 × Z2 global symmetry which protects the ground state degeneracy of cluster states for open boundary conditions. Such a degeneracy ultimately arises because the set of stabilizers do not span a complete set of integrals of motion of the cluster state Hamiltonian for open boundary conditions. By applying control phase transformations, our construction makes the stabilizers into the Pauli operators spanning the qubit Hilbert space from which the degeneracy comes. © Springer Science+Business Media, LLC 2011.

## When Casimir meets Kibble-Zurek

PHYSICA SCRIPTA **T151** (2012) ARTN 014071

## 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.

## 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.

## 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)

## 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.

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

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

We introduce a bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the stochastic local operations and classical communication protocols familiar in quantum information. Although the mathematical methods are the same, the meaning of the gauge group is different. The measure we introduce, "twist," is constructed as a Wilson loop from a correlation-induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state using local operations, the twistedness is given by a nontrivial element of the Lorentz group, the correlation-induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary nontrivial loop one can imagine. © 2011 American Physical Society.