# Publications

## Quantum correlations which imply causation

Scientific Reports Nature Publishing Group **5** (2015) 18281

In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable [1]: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.

## Non-Hermitian Dynamics in the Quantum Zeno Limit

arXiv (2015)

Measurement is one of the most counter-intuitive aspects of quantum physics. Frequent measurements of a quantum system lead to quantum Zeno dynamics where time evolution becomes confined to a subspace defined by the projections. However, weak measurement performed at a finite rate is also capable of locking the system into such a Zeno subspace in an unconventional way: by Raman-like transitions via virtual intermediate states outside this subspace, which are not forbidden. Here, we extend this concept into the realm of non-Hermitian dynamics by showing that the stochastic competition between measurement and a system's own dynamics can be described by a non-Hermitian Hamiltonian. We obtain an analytic solution for ultracold bosons in a lattice and show that a dark state of the tunnelling operator is a steady state in which the observable's fluctuations are zero and tunnelling is suppressed by destructive matter-wave interference. This opens a new venue of investigation beyond the canonical quantum Zeno dynamics and leads to a new paradigm of competition between global measurement backaction and short-range atomic dynamics.

## Quantum measurement-induced antiferromagnetic order and density modulations in ultracold Fermi gases in optical lattices

arXiv (2015)

We show that global light scattering from ultracold fermions in an optical lattice into a cavity can be used for tailoring local properties of the atomic system. Quantum measurement backaction strongly affects the evolution of the atoms and leads to quantum states with spatial modulations of the density and magnetisation. We propose different detection schemes for realising antiferromagnetic states and density waves. We demonstrate that such long-range correlations are a consequence of the global but spatially structured measurement backaction and cannot be realized with local addressing.

## Classification of macroscopic quantum effects

Optics Communications Elsevier **337** (2015) 22–26-

We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of systems differ so widely, we use a case by case approach to identifying the different parameters and criteria that capture their behaviour in a quantum mechanical framework. We find it helpful to categorise systems into three broad classes defined by mass, spatio-temporal coherence, and number of particles. The classes are not mutually exclusive and in fact the properties of some systems fit into several classes. We discuss experiments by turn, starting with interference of massive objects like macromolecules and micro-mechanical resonators, followed by self-interference of single particles in complex molecules, before examining the striking advances made with superconducting qubits. Finally, we propose a theoretical basis for quantifying the macroscopic features of a system to lay the ground for a more systematic comparison of the quantum properties in disparate systems.

## Replicating the benefits of Deutschian closed timelike curves without breaking causality

NPJ QUANTUM INFORMATION **1** (2015) ARTN 15007

## Universal optimal quantum correlator

International Journal of Quantum Information (2015)

© 2015 World Scientific Publishing Company. Recently, a novel operational strategy to access quantum correlation functions of the form Tr[AρB] was provided in [F. Buscemi, M. Dall'Arno, M. Ozawa and V. Vedral, arXiv:1312.4240]. Here we propose a realization scheme, that we call partial expectation values, implementing such strategy in terms of a unitary interaction with an ancillary system followed by the measurement of an observable on the ancilla. Our scheme is universal, being independent of ρ, A, and B, and it is optimal in a statistical sense. Our scheme is suitable for implementation with present quantum optical technology, and provides a new way to test uncertainty relations.

## Majorana transport in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings.

Journal of physics. Condensed matter : an Institute of Physics journal **27** (2015) 225302-

The tunneling experiment is a key technique for detecting Majorana fermion (MF) in solid state systems. We use Keldysh non-equilibrium Green function method to study two-lead tunneling in superconducting nanowire with Rashba and Dresselhaus spin-orbit couplings. A zero-bias dc conductance peak appears in our setup which signifies the existence of MF and is in accordance with previous experimental results on InSb nanowire. Interestingly, due to the exotic property of MF, there exists a hole transmission channel which makes the currents asymmetric at the left and right leads. The ac current response mediated by MF is also studied here. To discuss the impacts of Coulomb interaction and disorder on the transport property of Majorana nanowire, we use the renormalization group method to study the phase diagram of the wire. It is found that there is a topological phase transition under the interplay of superconductivity and disorder. We find that the Majorana transport is preserved in the superconducting-dominated topological phase and destroyed in the disorder-dominated non-topological insulator phase.

## Classification of macroscopic quantum effects

Optics Communications **337** (2015) 22-26

© 2014 Elsevier B.V. All rights reserved. We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of systems differ so widely, we use a case by case approach to identifying the different parameters and criteria that capture their behaviour in a quantum mechanical framework. We find it helpful to categorise systems into three broad classes defined by mass, spatio-temporal coherence, and number of particles. The classes are not mutually exclusive and in fact the properties of some systems fit into several classes. We discuss experiments by turn, starting with interference of massive objects like macromolecules and micro-mechanical resonators, followed by self-interference of single particles in complex molecules, before examining the striking advances made with superconducting qubits. Finally, we propose a theoretical basis for quantifying the macroscopic features of a system to lay the ground for a more systematic comparison of the quantum properties in disparate systems.

## Probing matter-field and atom-number correlations in optical lattices by global nondestructive addressing

PHYSICAL REVIEW A **92** (2015) ARTN 013613

## Towards witnessing quantum effects in complex molecules.

Faraday discussions **184** (2015) 183-191

Whether many-body objects like organic molecules can exhibit full quantum behaviour, including entanglement, is an open fundamental question. We present a generic theoretical protocol for entangling two organic molecules, such as dibenzoterrylene in anthracene. The availability of organic dye molecules with two-level energy structures characterised by sharp and intense emission lines are characteristics that position them favourably as candidates for quantum information processing technologies involving single-photons. Quantum entanglement can in principle be generated between several organic molecules by carefully interfering their photoluminescence spectra. Major milestones have been achieved in the last 10 years showcasing entanglement in diverse systems including ions, cold atoms, superconductors, photons, quantum dots and NV-centres in diamond, but not yet in molecules.

## Generalized Pauli constraints: Hierarchy of pinning and quasipinning-measure

arXiv (2015)

The Pauli exclusion principle (PEP) has a tremendous impact on the properties and the behavior of most fermionic quantum systems. Remarkably, even stronger restrictions on fermionic natural occupation numbers follow from the fermionic exchange statistics. Based on a hierarchy induced by PEP we develop an operationally meaningful measure which allows to quantify the potential physical relevance of those generalized Pauli constraints (GPC) beyond the well-established relevance of PEP. By studying a few fermions in a harmonic trap we explore and confirm for the first time such nontrivial significance of GPC not only for weak couplings but even up to medium interaction strengths.

## A measure of majorization emerging from single-shot statistical mechanics

NEW JOURNAL OF PHYSICS **17** (2015) ARTN 073001

## Quantum optics, molecular spectroscopy and low-temperature spectroscopy: general discussion.

Faraday discussions **184** (2015) 275-303

## Maxwell's daemon: information versus particle statistics

Scientific Reports Springer Nature **4** (2014) 6995

Maxwell's daemon is a popular personification of a principle connecting information gain and extractable work in thermodynamics. A Szilard Engine is a particular hypothetical realization of Maxwell's daemon, which is able to extract work from a single thermal reservoir by measuring the position of particle(s) within the system. Here we investigate the role of particle statistics in the whole process; namely, how the extractable work changes if instead of classical particles fermions or bosons are used as the working medium. We give a unifying argument for the optimal work in the different cases: the extractable work is determined solely by the information gain of the initial measurement, as measured by the mutual information, regardless of the number and type of particles which constitute the working substance.

## Topological quantum phase transitions in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings

ANNALS OF PHYSICS **349** (2014) 189-200

## Guaranteed energy-efficient bit reset in finite time.

Physical review letters **113** (2014) 100603-

Landauer's principle states that it costs at least kBTln2 of work to reset one bit in the presence of a heat bath at temperature T. The bound of kBTln2 is achieved in the unphysical infinite-time limit. Here we ask what is possible if one is restricted to finite-time protocols. We prove analytically that it is possible to reset a bit with a work cost close to kBTln2 in a finite time. We construct an explicit protocol that achieves this, which involves thermalizing and changing the system's Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover, we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time.

## Guaranteed Energy-Efficient Bit Reset in Finite Time (vol 113, 100603, 2014)

PHYSICAL REVIEW LETTERS **113** (2014) ARTN 169901

## Towards quantifying complexity with quantum mechanics

EUROPEAN PHYSICAL JOURNAL PLUS **129** (2014) ARTN 191

## Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems

PHYSICAL REVIEW X **4** (2014) ARTN 041028