# Publications

## Observing the operational significance of discord consumption

Nature Physics **8** (2012) 671-675

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this quantum advantage'. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource. © 2012 Macmillan Publishers Limited. All rights reserved.

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

Communications in Mathematical Physics (2012) 1-47

## A functional interpretation of continuous variable quantum discord

2011 Int. Quantum Electron. Conf., IQEC 2011 and Conf. Lasers and Electro-Optics, CLEO Pacific Rim 2011 Incorporating the Australasian Conf. Optics, Lasers and Spectroscopy and the Australian Conf. (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 IEEE.

## 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.

## Natural mode entanglement as a resource for quantum communication

AIP Conference Proceedings **1363** (2011) 299-302

Natural particle-number entanglement resides between spatial modes in coherent ultracold atomic gases. However, operations on the modes are restricted by a superselection rule that forbids coherent superpositions of different particle numbers. This would seemingly prevent mode entanglement from being used as a resource for quantum communication. Here I demonstrate that mode entanglement of a single massive particle can be used for dense coding despite the superselection rule if both parties share a coherent reservoir. © 2011 American Institute of Physics.

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

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

We consider the light scattering from ultracold atoms trapped in an optical lattice inside a cavity. In such a system, both the light and atomic motion should be treated in a fully quantum mechanical way. The unitary evolution of the light-matter quantum state is shown to demonstrate the non-trivial phase dependence, quadratic in the atom number. This is essentially due to the dynamical self-consistent nature of the light modes assumed in our model. The collapse of the quantum state during the photocounting process is analyzed as well. It corresponds to the measurement-induced atom number squeezing. We show that, at the final stage of the state collapse, the shrinking of the width of the atom number distribution behaves exponentially in time. This is much faster than the square root time dependence, obtained for the initial stage of the state collapse. The exponentially fast squeezing appears due to the discrete nature of the atom number distribution. © 2011 Pleiades Publishing, Ltd.

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

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

## Merging quantum optics and quantum many-body atomic systems

2011 Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference, CLEO EUROPE/EQEC 2011 (2011)

A system joining the problems of quantum optics and quantum gases - ultracold atoms trapped in an optical lattice inside a cavity - is considered. Thus, the quantum natures of both the light and atomic motion play equally important roles in the process [1-4]. This is in striking contrast to the majority of theoretical and experimental problems on ultracold gases, where the role of light is reduced to a classical auxiliary tool for trapping and manipulating intriguing atomic states. © 2011 IEEE.

## Unification of quantum and classical correlations and quantumness measures

AIP Conference Proceedings **1384** (2011) 69-75

We give a pedagogical introduction to quantum discord and discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy. This allows us to put all correlations on an equal footing. Entanglement and dissonance jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We finally show, using relative entropy, how different notions of quantum correlations are related to each other. This gives a single theory that incorporates all correlations, quantum and classical, and different methods of quantifying them. © 2011 American Institute of Physics.

## 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.

## Behavior of entanglement and Cooper pairs under relativistic boosts

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

Recent work has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single-particle results to multiparticle entanglements by focusing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet states acquire a singlet component, the size of which depends on the geometry. This transformation between the different singlet and triplet superconducting pairs may lead to a better understanding of unconventional superconductivity. © 2011 American Physical Society.

## 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.

## Merging quantum optics and quantum many-body atomic systems

Optics InfoBase Conference Papers (2011)