arXiv subjects

David Jennings

Publications and source records attributed to David Jennings.

At least 55 records · Page 3Linked to original sources

arXiv2014

Exchange Fluctuation Theorem for correlated quantum systems

We extend the Exchange Fluctuation Theorem for energy exchange between thermal quantum systems beyond the assumption of molecular chaos, and describe the non-equilibrium exchange dynamics of correlated quantum states. The relation quantifies how the tendency for systems to equilibrate is modified in high-correlation environments. Our results elucidate the role of measurement disturbance for such scenarios. We show a simple application by finding a semi-classical maximum work theorem in the presence of correlations.

quant-ph↗

arXiv2014

Reexamination of Pure Qubit Work Extraction

Many work extraction or information erasure processes in the literature involve the raising and lowering of energy levels via external fields. But even if the actual system is treated quantum mechanically, the field is assumed to be classical and of infinite strength, hence not developing any correlations with the system or experiencing back-actions. We extend these considerations to a fully quantum mechanical treatment, by studying a spin-1/2 particle coupled to a finite-sized directional quantum reference frame, a spin-l system, which models an external field. With this concrete model together with a bosonic thermal bath, we analyse the back-action a finite-size field suffers during a quantum-mechanical work extraction process, the effect this has on the extractable work, and highlight a range of assumptions commonly made when considering such processes. The well-known semi-classical treatment of work extraction from a pure qubit predicts a maximum extractable work W = kT log 2 for a quasi-static process, which holds as a strict upper bound in the fully quantum mechanical case, and is only attained in the classical limit. We also address the problem of emergent local time-dependence in a joint system with globally fixed Hamiltonian.

quant-ph↗

arXiv2014

Quantum correlations of two-qubit states with one maximally mixed marginal

We investigate the entanglement, CHSH nonlocality, fully entangled fraction and symmetric extendibility of two-qubit states that have a single maximally mixed marginal. Within this set of states, the steering ellipsoid formalism has recently highlighted an interesting family of so-called 'maximally obese' states. These are found to have extremal quantum correlation properties that are significant in the steering ellipsoid picture and for the study of two-qubit states in general.

quant-ph↗

arXiv2014

Quantum Steering Ellipsoids

The quantum steering ellipsoid of a two-qubit state is the set of Bloch vectors that Bob can collapse Alice's qubit to, considering all possible measurements on his qubit. We provide an elementary construction of the ellipsoid for arbitrary states, calculate its volume, and explain how this geometric representation can be made faithful. The representation provides a range of new results, and uncovers new features, such as the existence of "incomplete steering" in separable states. We show that entanglement can be analysed in terms of three geometric features of the ellipsoid, and prove that a state is separable if and only if it obeys a "nested tetrahedron" condition.

quant-ph↗

arXiv2014

Operational constraints on state-dependent formulations of quantum error-disturbance trade-off relations

We argue for an operational requirement that all state-dependent measures of disturbance should satisfy. Motivated by this natural criterion, we prove that in any $d$-dimensional Hilbert space and for any pair of non-commuting operators, $A$ and $B$, there exists a set of at least $2^{d-1}$ zero-noise, zero-disturbance (ZNZD) states, for which the first observable can be measured without noise and the second will not be disturbed. Moreover, we show that it is possible to construct such ZNZD states for which the expectation value of the commutator $[A,B]$ does not vanish. Therefore any state-dependent error-disturbance relation, based on the expectation value of the commutator as a lower bound, must violate the operational requirement. We also discuss Ozawa's state-dependent error-disturbance relation in light of our results and show that the disturbance measure used in this relation exhibits unphysical properties. We conclude that the trade-off is inevitable only between state-independent measures of error and disturbance.

quant-ph↗

arXiv2014

Quantum and classical entropic uncertainty relations

How much of the uncertainty in predicting measurement outcomes for non-commuting quantum observables is genuinely quantum mechanical? We provide a natural decomposition of the total entropic uncertainty of two non-commuting observables into a classical component, and an intrinsically quantum mechanical component. We show that the total quantum component in a state is never lower or upper bounded by any state-independent quantities, but instead admits "purity-based" lower bounds that generalize entropic formulations such as the Maassen-Uffink relation. These relations reveal a non-trivial interplay between quantum and classical randomness in any finite-dimensional state.

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arXiv2012

Distinct Quantum States Can Be Compatible with a Single State of Reality

Perhaps the quantum state represents information about reality, and not reality directly. Wave function collapse is then possibly no more mysterious than a Bayesian update of a probability distribution given new data. We consider models for quantum systems with measurement outcomes determined by an underlying physical state of the system but where several quantum states are consistent with a single underlying state---i.e., probability distributions for distinct quantum states overlap. Significantly, we demonstrate by example that additional assumptions are always necessary to rule out such a model.

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arXiv2012

The continuum limit of a tensor network: a path integral representation

We argue that the natural way to generalise a tensor network variational class to a continuous quantum system is to use the Feynman path integral to implement a continuous tensor contraction. This approach is illustrated for the case of a recently introduced class of quantum field states known as continuous matrix-product states (cMPS). As an example of the utility of the path-integral representation we argue that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. An argument that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity is also provided.

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arXiv2012

On the spectral dependence of separable and classical correlations in small quantum systems

We study the correlation structure of separable and classical states in 2x2- and 2x3-dimensional quantum systems with fixed spectra. Even for such simple systems the maximal correlation - as measured by mutual information - over the set of unitarily accessible separable states is highly non-trivial to compute; however for the 2x2 case a particular class of spectra admits full analysis and allows us to contrast classical states with more general separable states. We analyse a particular entropic partial order on the set of spectra and prove for the qubit-qutrit case that this partial order alone picks out a unique classical maximum state for mutual information. Moreover the 2x3 case is the largest system with such a property.

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arXiv2012

The WAY theorem and the quantum resource theory of asymmetry

The WAY theorem establishes an important constraint that conservation laws impose on quantum mechanical measurements. We formulate the WAY theorem in the broader context of resource theories, where one is constrained to a subset of quantum mechanical operations described by a symmetry group. Establishing connections with the theory of quantum state discrimination we obtain optimal unitaries describing the measurement of arbitrary observables, explain how prior information can permit perfect measurements that circumvent the WAY constraint, and provide a framework that establishes a natural ordering on measurement apparatuses through a decomposition into asymmetry and charge subsystems.

quant-ph↗

arXiv2012

Quantum Mutual Information Along Unitary Orbits

Motivated by thermodynamic considerations, we analyse the variation of the quantum mutual information on a unitary orbit of a bipartite system's state, with and without global constraints such as energy conservation. We solve the full optimisation problem for the smallest system of two qubits, and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems, such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimisation displays non-trivial structures. We characterise a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular "Young tableau" form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a "see-saw effect" for these entropies forces a finer analysis to determine the optimal tableau.

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arXiv2012

Maximally and minimally correlated states attainable within a closed evolving system

The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation in correlations is useful. The optimization problem it raises requires us to search for the maximally and minimally correlated states on a unitary orbit, with and without energy conservation. This is fully solvable for the smallest system of two qubits. For larger systems the problem is reduced to a manageable, classical optimization.

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arXiv2011

Are right angles special? The optimal primitive reference frame

We consider the smallest possible directional reference frames allowed and determine the best one can ever do in preserving quantum information in various scenarios. We find that for the preservation of a single spin state, two orthogonal spins are optimal primitive reference frames, and in a product state do approximately 22% as well as an infinite-sized classical frame. By adding a small amount of entanglement to the reference frame this can be raised to 2(2/3)^5 = 26%. Under the different criterion of entanglement-preservation a very similar optimal reference frame is found, however this time for spins aligned at an optimal angle of 87 degrees. In this case 24% of the negativity is preserved. The classical limit is considered numerically, and indicates under the criterion of entanglement preservation, that 90 degrees is selected out non-monotonically, with a peak optimal angle of 96.5 degrees for L = 3 spins.

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arXiv2010

On the response of a particle detector in Anti-de Sitter spacetime

We consider the vacuum response of a particle detector in Anti-de Sitter spacetime, and in particular analyze how spacetime features such as curvature and dimensionality affect the response spectrum of an accelerated detector. We calculate useful limits on Wightman functions, analyze the dynamics of the detector in terms of vacuum fluctuations and radiation reactions, and discuss the thermalization process for the detector. We also present a generalization of the GEMS approach and obtain the Gibbons-Hawking temperature of de Sitter spacetime as an embedded Unruh temperature in a curved Anti-de Sitter spacetime.

gr-qc↗

arXiv2010

A Photonic Implementation for the Topological Cluster State Quantum Computer

A new implementation of the topological cluster state quantum computer is suggested, in which the basic elements are linear optics, measurements, and a two-dimensional array of quantum dots. This overcomes the need for non-linear devices to create a lattice of entangled photons. We give estimates of the minimum efficiencies needed for the detectors, fusion gates and quantum dots, from a numerical simulation.

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arXiv2010

Dynamics of a quantum reference frame undergoing selective measurements and coherent interactions

We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation which cannot be revealed by considering the averaged case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation which leads to quite different dynamics than the case of repeated measurements. We then consider strategies for correcting reference frame drift if we are given a set of particles with polarization opposite to the direction of drift. In particular, we find that by implementing a suitably chosen unitary interaction after every two measurements we can eliminate the rotational drift of the reference frame.

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arXiv2010

Entanglement and the Thermodynamic Arrow of Time

We discuss quantum entanglement in the context of the thermodynamic arrow of time. We review the role of correlations in entropy-decreasing events and prove that the occurrence of a transformation between two thermodynamic states constitutes a new type of entanglement witness, one not defined as a separating plane in state space between separable and entangled states, but as a physical process dependent on the local initial properties of the states. Extending work by Partovi, we consider a general entangled multipartite system that allows large reversals of the thermodynamic arrow of time. We describe a hierarchy of arrows that arises from the different correlations allowed in a quantum state and examine these features in the context of Maxwell's Demon. We examine in detail the case of three qubits, and also propose some simple experimental demonstrations possible with small numbers of qubits.

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arXiv2009

Transitions in the computational power of thermal states for measurement-based quantum computation

We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model.

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