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Jayne Thompson

Publications and source records attributed to Jayne Thompson.

At least 55 records · Page 3Linked to original sources
arXiv2018

A practical, unitary simulator for non-Markovian complex processes

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this letter we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process.

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arXiv2017

Geometry of quantum correlations in space-time

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of non-unital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states.

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arXiv2017

Operational effects of the UNOT gate on classical and quantum correlations

The NOT gate that flips a classical bit is ubiquitous in classical information processing. However its quantum analogue, the universal NOT (UNOT) gate that flips a quantum spin in any alignment into its antipodal counterpart is strictly forbidden. Here we explore the connection between this discrepancy and how UNOT gates affect classical and quantum correlations. We show that while a UNOT gate always preserves classical correlations between two spins, it can non-locally increase or decrease their shared discord in ways that allow violation of the data processing inequality. We experimentally illustrate this using a multi-level trapped \Yb ion that allows simulation of anti-unitary operations.

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arXiv2017

Unbounded memory advantage in stochastic simulation using quantum mechanics

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.

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arXiv2017

Experimental cyclic inter-conversion between Coherence and Quantum Correlations

Quantum resource theories seek to quantify sources of non-classicality that bestow quantum technologies their operational advantage. Chief among these are studies of quantum correlations and quantum coherence. The former to isolate non-classicality in the correlations between systems, the latter to capture non-classicality of quantum superpositions within a single physical system. Here we present a scheme that cyclically inter-converts between these resources without loss. The first stage converts coherence present in an input system into correlations with an ancilla. The second stage harnesses these correlations to restore coherence on the input system by measurement of the ancilla. We experimentally demonstrate this inter-conversion process using linear optics. Our experiment highlights the connection between non-classicality of correlations and non-classicality within local quantum systems, and provides potential flexibilities in exploiting one resource to perform tasks normally associated with the other.

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arXiv2017

The classical-quantum divergence of complexity in modelling spin chains

The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this measure exhibits drastically different behaviour: it rises to a maximum at some finite temperature then tends back towards zero for higher temperatures. This demonstrates how complexity, as captured by the amount of memory required to model a process, can exhibit radically different behaviour when quantum processing is allowed.

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arXiv2017

Thermodynamics of complexity and pattern manipulation

Many organisms capitalize on their ability to predict the environment to maximize available free energy, and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns - temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators -- devices that convert thermodynamic work to patterns or vice versa - and use them to build a 'pattern engine' that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices; the ones that exhibit desired operational behaviour while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation, and show that it is generally non-zero and connected with the pattern's intrinsic crypticity - a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behaviour reveals about its future, and the amount one needs to communicate about this past to optimally predict the future.

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arXiv2017

Using quantum theory to reduce the complexity of input-output processes

All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic abstractions of their input-output behavior that allow us to simulate how such systems can behave in the future, conditioned on what has transpired in the past. Here, we show that classical models cannot avoid inefficiency -- storing past information that is unnecessary for correct future simulation. We construct quantum models that mitigate this waste, whenever it is physically possible to do so. This suggests that the complexity of general input-output processes depends fundamentally on what sort of information theory we use to describe them.

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arXiv2016

Fragile states are better for quantum metrology

In quantum metrology, quantum probe states are capable of estimating unknown physical parameters to precisions beyond classical limits. What qualities do such states possess? Here we relate the performance of a probe state at estimating a parameter $ϕ$ -- as quantified by the quantum Fisher information -- to the amount of purity it loses when $ϕ$ undergoes statistical fluctuation. This indicates that the better a state is for estimating $ϕ$, the more it decoheres when $ϕ$ is subject to noise.

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arXiv2016

The power of one qumode for quantum computation

Although quantum computers are capable of solving problems like factoring exponentially faster than the best-known classical algorithms, determining the resources responsible for their computational power remains unclear. An important class of problems where quantum computers possess an advantage is phase estimation, which includes applications like factoring. We introduce a new computational model based on a single squeezed state resource that can perform phase estimation, which we call the power of one qumode. This model is inspired by an interesting computational model known as deterministic quantum computing with one quantum bit (DQC1). Using the power of one qumode, we identify that the amount of squeezing is sufficient to quantify the resource requirements of different computational problems based on phase estimation. In particular, it establishes a quantitative relationship between the resources required for factoring and DQC1. For example, we find the squeezing required to factor has an exponential scaling whereas no squeezing (i.e., a coherent state) is already sufficient to solve the hardest problem in DQC1.

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arXiv2016

How Discord underlies the Noise Resilience of Quantum Illumination

The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord - a more resilient form of quantum correlations - explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discord's role preserving the benefits of entanglement in entanglement breaking noise.

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arXiv2015

Quantum information approach to Bose-Einstein condensation of composite bosons

We consider composite bosons (cobosons) comprised of two elementary particles, fermions or bosons, in an entangled state. First, we show that the effective number of cobosons implies the level of correlation between the two constituent particles. For the maximum level of correlation, the effective number of cobosons is the same as the total number of cobosons, which can exhibit the original Bose-Einstein condensation (BEC). In this context, we study a model of BEC for indistinguishable cobosons with a controllable parameter, i.e., entanglement between the two constituent particles. We find that bi-fermions behave in a predictable way, i.e., the effective number of the ground state coboson is an increasing function of entanglement between a pair of constituent fermions. Interestingly, bi-bosons exhibit the opposite behaviour - the effective number of the ground state coboson is a decreasing function of entanglement between a pair of constituent bosons.

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arXiv2015

Delayed Choice Contextuality: A way to rule out Contextual Hidden Variables

A PhD student is locked inside a box, imitating a quantum system by mimicking the measurement statistics of any viable observable nominated by external observers. Inside a second box lies a genuine quantum system. Either box can be used to pass a test for contextuality - and from the perspective of an external observer, be operationally indistinguishable. There is no way to discriminate between the two boxes based on the output statistics of any contextuality test. This poses a serious problem for contextuality tests to be used as viable tests for device independent quantumness, and severely limits realistic use of contextuality as an operational resource. Here we rectify this problem by building experimental techniques for distinguishing a contextual system that is genuinely quantum, and one that mimics it through clever use of hidden variables.

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arXiv2014

Replicating the benefits of closed timelike curves without breaking causality

In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level, resolving such paradoxes induce radical benefits - from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states - even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil the subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.

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arXiv2014

Towards Quantifying Complexity with Quantum Mechanics

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified by the complexity of its simplest mathematical model - the model that requires the least past information for optimal future prediction. Here we review how such models, known as $ε$-machines can be further simplified through quantum logic, and explore the resulting consequences for understanding complexity. In particular, we propose a new measure of complexity based on quantum $ε$-machines. We apply this to a simple system undergoing constant thermalization. The resulting quantum measure of complexity aligns more closely with our intuition of how complexity should behave.

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arXiv2013

Coherent states of composite bosons

We present a systematic analysis on coherent states of composite bosons consisting of two distinguishable particles. By defining an effective composite boson (coboson) annihilation operator, we derive its eigenstate and commutator. Depending on the elementary particles comprising the composite particles, we gauge the resemblance between this eigenstate and traditional coherent states through typical measures of nonclassicality, such as quadrature variances and Mandel's Q parameter. Furthermore, we show that the eigenstate of the coboson annihilation operator is useful in estimating the maximum eigenvalue of the coboson number operator.

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arXiv2013

Quantum Computing with black-box Subroutines

Modern programming relies on our ability to treat preprogrammed functions as black boxes - we can invoke them as subroutines without knowing their physical implementation. Here we show it is generally impossible to execute an unknown quantum subroutine. This, as a special case, forbids applying black-box subroutines conditioned on an ancillary qubit. We explore how this limits many quantum algorithms - forcing their circuit implementation to be individually tailored to specific inputs and inducing failure if these inputs are not known in advance. We present a method to avoid this situation for certain computational problems. We apply this method to enhance existing quantum factoring algorithms; reducing their complexity, and the extent to which they need to be tailored to factor specific numbers. Thus, we highlight a natural property of classical information that fails in the advent of quantum logic; and simultaneously demonstrate how to mitigate its effects in practical situations.

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