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Kok Chuan Tan

Publications and source records attributed to Kok Chuan Tan.

At least 19 recordsLinked to original sources
arXiv2026

Achieving Heisenberg limit under noisy conditions with quantum Zeno dynamics and dynamical decoupling

Quantum Zeno dynamics (QZD) and dynamical decoupling (DD) are useful tools that enable the effective suppression of noise in quantum systems. We consider the problem of when (i) noise can be suppressed and (ii) Heisenberg limit (HL) can be achieved in quantum metrology, and prove necessary and sufficient conditions for when QZD and DD are useful for achieving these two goals. We further show this condition can hold even when the Hamiltonian-not-in-Lindblad-span (HNLS) condition fails, allowing QZD/DD to recover Heisenberg scaling beyond what is certified by the usual HNLS-based quantum error correction (QEC) criterion. Finally, we demonstrate that the combination of both techniques can allow individually imperfect QZD and DD strategies to saturate HL.

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arXiv2025

Restoring Heisenberg-Limited Precision in Non-Markovian Open Quantum Systems via Dynamical Decoupling

Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of such resources through decoherence. While significant progress has been made in mitigating Markovian noise, the extent to which non-Markovian noise can be mitigated remains poorly understood. We demonstrate that Heisenberg Scaling, the ultimate quantum limit on measurement precision, can be recovered in quantum metrology under non-Markovian noise by leveraging carefully designed Dynamical Decoupling Techniques. Importantly, our approach does not rely on assumptions of Markovian dynamics. By imposing appropriate conditions on the control Hamiltonian, we show that HS can be achieved irrespective of whether the noise is Markovian or non-Markovian. We also prove necessary and sufficient conditions for the existence of such control Hamiltonians. As an illustrative example, we apply our framework to the damped Jaynes-Cummings model, successfully mitigating memory effects and maintaining measurement precision in complex, non-Markovian environments. These findings highlight the power of quantum control to overcome decoherence challenges and enhance metrological performance in realistic, noisy quantum systems.

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arXiv2024

Kirkwood-Dirac Type Quasiprobabilities as Universal Identifiers of Nonclassical Quantum Resources

We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. This is achieved by demonstrating that it is always possible to identify a set of incompatible measurements that distinguishes between resourceful states and nonresourceful states. The quasiprobability reveals a resourceful quantum state by having at least one quasiprobabilty outcome with a strictly negative numerical value. We also show that there always exists a quasiprobabilty distribution where the total negativity can be interpreted as the geometric distance between a resourceful quantum state to the closest nonresourceful state. It can also be shown that Kirkwood-Dirac type quasiprobability distributions, like the Wigner distribution, can be made informationally complete, in the sense that it can provide complete information about the quantum state while simultaneously revealing nonclassicality whenever a quasiprobability outcome is negative. Moreover, we demonstrate the existence of sufficiently strong anomalous weak values whenever the quasiprobability distribution is negative, which suggests a means to experimentally test such quasiprobability distributions. Since incompatible measurements are necessary in order for the quasiprobability to be negative, this result suggests that measurement incompatibility may underlie any quantum advantage gained from utilizing a nonclassical quantum resource

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arXiv2021

Variational quantum algorithms to estimate rank, quantum entropies, fidelity and Fisher information via purity minimization

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing cost function gradients are also discussed.

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arXiv2021

Fisher information universally identifies quantum resources

We show that both the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories, in the sense that they can always distinguish between states with and without a given resource. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states. We provide bounds on the extent of this advantage, as well as a simple criterion to test whether different resources are useful for the estimation of unitarily encoded parameters. Finally, we extend the results to show that the Fisher information is also able to identify the dynamical resourcefulness of quantum operations.

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arXiv2021

Error mitigation in quantum metrology via zero noise extrapolation

We consider Zero Noise Extrapolation (ZNE) as an error mitigation strategy in quantum metrology. It is shown that noise expansion can be systematically performed over sufficiently short time scales for general Markovian noise models described by the time homogeneous Lindblad master equation. This suggests that ZNE can be an effective, resource efficient error mitigation alternative when strategies employing full quantum error correcting codes are unavailable. The ZNE method is then applied quantum phase estimation in a Mach-Zehnder interferometer subject to photon losses. Numerical simulations show a significant recovery of measurement sensitivity by employing first order ZNE corrections, which can be further improved upon using higher order corrections at the cost of additional measurements.

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arXiv2020

Quantum stochastic series expansion methods

A quantum implementation of the Stochastic Series Expansion (SSE) Monte Carlo method is proposed, and it is shown that quantum SSE offers significant advantages over classical implementations of SSE. In particular, for problems where classical SSE encounters the sign problem, the cost of implementing a Monte Carlo iteration scales only linearly with system size in quantum SSE, while it may scale exponentially with system size in classical SSE. In cases where classical SSE can be efficiently implemented, quantum SSE still offers an advantage by allowing for more general observables to be measured.

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arXiv2020

Fast quantum imaginary time evolution

A fast implementation of the quantum imaginary time evolution (QITE) algorithm called Fast QITE is proposed. The algorithmic cost of QITE typically scales exponentially with the number of particles it nontrivially acts on in each Trotter step. In contrast, a Fast QITE implementation reduces this to only a linear scaling. It is shown that this speed up leads to a quantum advantage when sampling diagonal elements of a matrix exponential, which cannot be achieved using the standard implementation of the QITE algorithm. Finally the cost of implementing Fast QITE for finite temperature simulations is also discussed.

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arXiv2020

Identifying quantum phase transitions via geometric measures of nonclassicality

In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of nonclassicality are sufficient conditions to identify phase transitions at arbitrary temperature. This establishes that geometric measures of nonclassicality, in any quantum resource theory, are generic tools to investigate phase transitions in quantum systems. At zero temperature, we show that geometric measures of quantum coherence are especially useful for identifying first order quantum phase transitions, and can be a particularly robust alternative to other approaches employing measures of quantum correlations.

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arXiv2019

Nonclassical Light and Metrological Power: An Introductory Review

In this review, we introduce the notion of quantum nonclassicality of light, and the role of nonclassicality in optical quantum metrology. The first part of the paper focuses on defining and characterizing the notion of nonclassicality and how it may be quantified in radiation fields. Several prominent examples of nonclassical light is also discussed. The second part of the paper looks at quantum metrology through the lens of nonclassicality. We introduce key concepts such as the Quantum Fisher information, the Cram{é}r-Rao bound, the standard quantum limit and the Heisenberg limit, and discuss how nonclassical light may be exploited to beat classical limitations in high precision measurements. The discussion here will be largely theoretical, with some references to specific experimental implementations.

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arXiv2019

Negativity of quasiprobability distributions as a measure of nonclassicality

We demonstrate that the negative volume of any $s$-paramatrized quasiprobability, including the Glauber-Sudashan $P$-function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical monotones. These measures therefore belong to an operational resource theory of nonclassicality based on linear optical operations. The negativity of the Glauber-Sudashan $P$-function in particular can be shown to have an operational interpretation as the robustness of nonclassicality. We then introduce an approximate linear optical monotone, and show that this nonclassicality quantifier is computable and is able to identify the nonclassicality of nearly all nonclassical states.

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arXiv2019

Nonclassicality as a Quantifiable Resource for Quantum Metrology

We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state with moderate nonclassicality. This suggests that metrological power is related to the degree of quantum macroscopicity. Finally, we demonstrate that metrological resources useful for nonclassical displacement sensing tasks can be always converted into a useful resource state for phase sensitivity beyond the classical limit.

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arXiv2018

Nontrivial quantum observables can always be optimized via some form of coherence

In this paper we consider quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. As such, for any nontrivial observable, there exists a set of preferred basis states where the superposition between such states is always useful for optimizing a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then shown to be efficiently computable via a semidefinite program. We also show that these coherence measures respect a hierarchy that gives the robustness of coherence and the $l_1$ norm of coherence additional operational significance in terms of such optimization tasks.

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arXiv2018

Entanglement as the symmetric portion of correlated coherence

We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of coherence based entanglement monotones, which is always computable for pure states if the coherence measure is also computable. It is already known that every entanglement measure can be constructed as a coherence measure. The results presented here show that the converse is also true. The constructions that are presented can also be extended to also include more general notions of nonclassical correlations, leading to quantifiers that are related to quantum discord.

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arXiv2018

Coherence, Quantum Fisher Information, Superradiance and Entanglement are Interconvertible Resources

We demonstrate that quantum Fisher information and superradiance can be formulated as coherence measures in accordance with the resource theory of coherence, thus establishing a direct link between metrological information, superradiance and coherence. We also show that the trivial coherence measure has a metrological interpretation. The arguments are then generalized to show that coherence may be considered as the underlying fundamental resource for any functional of state that is first of all faithful, and second of all concave or linear. Arguments are then presented that show quantum Fisher information and the superradiant quantity are in fact antithetical resources in the sense that if coherence were directed to saturate one quantity, then it must come at the expense of the other. Finally, a key result of the paper is to demonstrate that coherence, quantum Fisher information, superradiant quantity, and entanglement are mutually interconvertible resources under incoherent operations.

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arXiv2018

Coherence, Asymmetry, and Quantum Macroscopicity

We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a weighted sum of asymmetry in each mode can be applied as a measure of macroscopic coherence. To exclude the effects of microscopic superpositions, we suggest a method to introduce a cutoff to the weighted sum that will specify the macroscopic portion of the coherence. This cutoff may be interpreted as the fuzziness for a given measurement outcome. Based on the suggested measures, we investigate the quantum macroscopicity for particular concrete examples in N-partite spin systems.

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arXiv2017

Disturbance-Based Measure of Macroscopic Coherence

We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent results when considering certain states such as a product of microscopic superpositions. An inequality relation is proved that relates the Wigner-Yanase-Dyson skew information and the measurement disturbance, providing arguments as to why our approach is able to rule out such inconsistencies. We show that our measure can also quantify the fragility of a quantum state to a certain type of decoherence. Our work provides a general framework of quantifying macroscopic coherence from an operational point of view, based on the relationship between the precision of the measurement and disturbance of the quantum state.

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