arXiv subjects

Ping Koy Lam

Publications and source records attributed to Ping Koy Lam.

At least 55 records · Page 3Linked to original sources

arXiv2024

Comparison of estimation limits for quantum two-parameter estimation

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cramér--Rao bound (e.g., the quantum Cramér--Rao bound and the Nagaoka Cram'er--Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu--Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cramér--Rao bound and the Lu--Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu--Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu--Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean squared error). The results offer insights into the general attainability and applicability of the Lu--Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings.

quant-ph↗

arXiv2024

Improving Gaussian channel simulation using non-unity gain heralded quantum teleportation

Gaussian channel simulation is an essential paradigm in understanding the evolution of bosonic quantum states. It allows us to investigate how such states are influenced by the environment and how they transmit quantum information. This makes it an essential tool for understanding the properties of Gaussian quantum communication. Quantum teleportation provides an avenue to effectively simulate Gaussian channels such as amplifier channels, loss channels and classically additive noise channels. However, implementations of these channels, particularly quantum amplifier channels and channels capable of performing Gaussian noise suppression are limited by experimental imperfections and non-ideal entanglement resources. In this work, we overcome these difficulties using a heralded quantum teleportation scheme that is empowered by a measurement-based noiseless linear amplifier. The noiseless linear amplification enables us to simulate a range of Gaussian channels that were previously inaccessible. In particular, we demonstrate the simulation of non-physical Gaussian channels otherwise inaccessible using conventional means. We report Gaussian noise suppression, effectively converting an imperfect quantum channel into a near-identity channel. The performance of Gaussian noise suppression is quantified by calculating the transmitted entanglement.

quant-ph↗

arXiv2024

The relative entropy of coherence quantifies performance in Bayesian metrology

The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This `coherence' is rigorously quantified by resource theories, which aim to understand how such properties may be exploited in quantum technologies. There has been much research on what the resource theory of coherence can reveal about quantum metrology, almost all of which has been from the viewpoint of Fisher information. We prove however that the relative entropy of coherence, and its recent generalisation to POVMs, naturally quantify the performance of Bayesian metrology. In particular, we show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence is equal to the difference between the information gained, and the optimal Holevo information. We call this relation the CXI equality. The ensemble coherence lets us visualise how much information is locked away in superposition inaccessible with a given measurement scheme, and quantify the advantage that would be gained by using a joint measurement on multiple states. Our results hold regardless of how the parameter is encoded in the state, encompassing unitary, dissipative, and discrete settings. We consider both projective measurements, and general POVMs. This work suggests new directions for research in quantum resource theories, provides a novel operational interpretation for the relative entropy of coherence and its POVM generalisation, and introduces a new tool to study the role of quantum features in metrology.

quant-ph↗

arXiv2024

Comparison of Discrete Variable and Continuous Variable Quantum Key Distribution Protocols with Phase Noise in the Thermal-Loss Channel

Discrete-variable (DV) quantum key distribution (QKD) based on single-photon detectors and sources have been successfully deployed for long-range secure key distribution. On the other hand, continuous-variable (CV) quantum key distribution (QKD) based on coherent detectors and sources is currently lagging behind in terms of loss and noise tolerance. An important discerning factor between DV-QKD and CV-QKD is the effect of phase noise, which is known to be more relevant in CV-QKD. In this article, we investigate the effect of phase noise on DV-QKD and CV-QKD protocols, including the six-state protocol and squeezed-state protocol, in a thermal-loss channel but with the assumed availability of perfect sources and detectors. We find that in the low phase noise regime but high thermal noise regime, CV-QKD can tolerate more loss compared to DV-QKD. We also compare the secret key rate as an additional metric for the performance of QKD. Requirements for this quantity to be high vastly extend the regions at which CV-QKD performs better than DV-QKD. Our analysis addresses the questions of how phase noise affects DV-QKD and CV-QKD and why the former has historically performed better in a thermal-loss channel.

quant-ph↗

arXiv2024

Verifying the security of a continuous variable quantum communication protocol via quantum metrology

Quantum mechanics offers the possibility of unconditionally secure communication between multiple remote parties. Security proofs for such protocols typically rely on bounding the capacity of the quantum channel in use. In a similar manner, Cramér-Rao bounds in quantum metrology place limits on how much information can be extracted from a given quantum state about some unknown parameters of interest. In this work we establish a connection between these two areas. We first demonstrate a three-party sensing protocol, where the attainable precision is dependent on how many parties work together. This protocol is then mapped to a secure access protocol, where only by working together can the parties gain access to some high security asset. Finally, we map the same task to a communication protocol where we demonstrate that a higher mutual information can be achieved when the parties work collaboratively compared to any party working in isolation.

quant-ph↗

arXiv2024

Role of the extended Hilbert space in the attainability of the Quantum Cramér-Rao bound for multiparameter estimation

The symmetric logarithmic derivative Cramér-Rao bound (SLDCRB) provides a fundamental limit to the minimum variance with which a set of unknown parameters can be estimated in an unbiased manner. It is known that the SLDCRB can be saturated provided the optimal measurements for the individual parameters commute with one another. However, when this is not the case the SLDCRB cannot be attained in general. In the experimentally relevant setting, where quantum states are measured individually, necessary and sufficient conditions for when the SLDCRB can be saturated are not known. In this setting the SLDCRB is attainable provided the SLD operators can be chosen to commute on an extended Hilbert space. However, beyond this relatively little is known about when the SLD operators can be chosen in this manner. In this paper we present explicit examples which demonstrate novel aspects of this condition. Our examples demonstrate that the SLD operators commuting on any two of the following three spaces: support space, support-kernel space and kernel space, is neither a necessary nor sufficient condition for commutativity on the extended space. We present a simple analytic example showing that the Nagaoka-Hayashi Cramér-Rao bound is not always attainable. Finally, we provide necessary and sufficient conditions for the attainability of the SLDCRB in the case when the kernel space is one-dimensional. These results provide new information on the necessary and sufficient conditions for the attainability of the SLDCRB.

quant-ph↗

arXiv2024

An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation

The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz comprising a problem and mixer Hamiltonian, with the parameters being classically optimised. While QAOA can be implemented on NISQ devices, physical limitations can limit circuit depth and decrease performance. To address these limitations, this work introduces the eXpressive QAOA (XQAOA), an overparameterised variant of QAOA that assigns more classical parameters to the ansatz to improve its performance at low depths. XQAOA also introduces an additional Pauli-Y component in the mixer Hamiltonian, allowing the mixer to implement arbitrary unitary transformations on each qubit. To benchmark the performance of XQAOA at unit depth, we derive its closed-form expression for the MaxCut problem and compare it to QAOA, Multi-Angle QAOA (MA-QAOA), a classical-relaxed algorithm, and the state-of-the-art Goemans-Williamson algorithm on a set of unweighted regular graphs with 128 and 256 nodes for degrees ranging from 3 to 10. Our results indicate that at unit depth, XQAOA has benign loss landscapes, allowing it to consistently outperform QAOA, MA-QAOA, and the classical-relaxed algorithm on all graph instances and the Goemans-Williamson algorithm on graph instances with degrees greater than 4. Small-scale simulations also reveal that unit-depth XQAOA surpasses both QAOA and MA-QAOA on all tested depths up to five. Additionally, we find an infinite family of graphs for which XQAOA solves MaxCut exactly and analytically show that for some graphs in this family, XQAOA achieves a much larger approximation ratio than QAOA. Overall, XQAOA is a more viable choice for variational quantum optimisation on NISQ devices, offering competitive performance at low depths.

quant-ph↗

arXiv2023

Quantum-optimal information encoding using noisy passive linear optics

The amount of information that a noisy channel can transmit has been one of the primary subjects of interest in information theory. In this work we consider a practically-motivated family of optical quantum channels that can be implemented without an external energy source. We optimize the Holevo information over procedures that encode information in attenuations and phase-shifts applied by these channels on a resource state of finite energy. It is shown that for any given input state and environment temperature, the maximum Holevo information can be achieved by an encoding procedure that uniformly distributes the channel's phase-shift parameter. Moreover for large families of input states, any maximizing encoding scheme has a finite number of channel attenuation values, simplifying the codewords to a finite number of rings around the origin in the output phase space. The above results and numerical evidence suggests that this property holds for all resource states. Our results are directly applicable to the quantum reading of an optical memory in the presence of environmental thermal noise.

quant-ph↗

arXiv2023

Modeling Photothermal Effects in High Power Optical Resonators used for Coherent Levitation

Radiation pressure can be used to enable optomechanical control and manipulation of the quantum state of a mechanical oscillator. Optomechanical interaction can also be mediated by photothermal effects which, although frequently overlooked, may compete with radiation pressure interaction. Understanding of how these phenomena affect the coherent exchange of information between optical and mechanical degrees of freedom is often underdeveloped, particularly in mesoscale high-power systems where photothermal effects can fully dominate the interaction. Here we report an effective theoretical model to predict and successfully reconstruct the dynamics of a unique optomechanical system: a cavity-enhanced setup for macroscopic optical levitation, where a free-standing mirror acts as the optomechanical oscillator. We decompose the photothermal interaction into two opposing light-induced effects, photothermal expansion, and thermo-optic effects. We then reconstruct a heuristic model that links the intracavity field to four types of cavity length changes caused by acoustic ($x_\textrm{ac}$), centre of mass ($x_\textrm{lev}$), photothermal ($x_\textrm{ex}$) and thermo-optic ($x_\textrm{re}$) displacements. This offers refined predictions with a higher degree of agreement with experimental results. Our work provides a mean to precisely model the photothermal effect of high power optomechanical systems, as well as for developing more precise photothermal modelling of photonics systems for precision sensing and quantum measurements.

physics.optics↗

arXiv2023

Twisted van der Waals Quantum Materials: Fundamentals, Tunability and Applications

Twisted vdW quantum materials have emerged as a rapidly developing field of 2D semiconductors. These materials establish a new central research area and provide a promising platform for studying quantum phenomena and investigating the engineering of novel optoelectronic properties such as single-photon emission, non-linear optical response, magnon physics, and topological superconductivity. These captivating electronic and optical properties result from, and can be tailored by, the interlayer coupling using moiré patterns formed by vertically stacking atomic layers with controlled angle misorientation or lattice mismatch. Their outstanding properties and the high degree of tunability position them as compelling building blocks for both compact quantum-enabled devices and classical optoelectronics. This article offers a comprehensive review of recent advancements in the understanding and manipulation of twisted van der Waals structures and presents a survey of the state-of-the-art research on moiré superlattices, encompassing interdisciplinary interests. It delves into fundamental theories, synthesis and fabrication, and visualization techniques, and the wide range of novel physical phenomena exhibited by these structures, with a focus on their potential for practical device integration in applications ranging from quantum information to biosensors, and including classical optoelectronics such as modulators, light emitting diodes (LEDs), lasers, and photodetectors. It highlights the unique ability of moiré superlattices to connect multiple disciplines, covering chemistry, electronics, optics, photonics, magnetism, topological and quantum physics. This comprehensive review provides a valuable resource for researchers interested in moiré superlattices, shedding light on their fundamental characteristics and their potential for transformative applications in various fields.

cond-mat.mtrl-sci↗

arXiv2023

Discriminating mixed qubit states with collective measurements

It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and implement strategies to optimally distinguish quantum states. In general, when we have access to multiple copies of quantum states the optimal measurement will be a collective measurement. However, to date, collective measurements have not been used to enhance quantum state discrimination. One of the main reasons for this is the fact that, in the usual state discrimination setting with equal prior probabilities, at least three copies of a quantum state are required to be measured collectively to outperform separable measurements. This is very challenging experimentally. In this work, by considering unequal prior probabilities, we propose and experimentally demonstrate a protocol for distinguishing two copies of single qubit states using collective measurements which achieves a lower probability of error than can be achieved by any non-entangling measurement. We implement our measurements on an IBM Q System One device, a superconducting quantum processor. Additionally, we implemented collective measurements on three and four copies of the unknown state and found they performed poorly.

quant-ph↗

arXiv2023

Mapping Guaranteed Positive Secret Key Rates for Continuous Variable Quantum Key Distribution

Continuous variable quantum key distribution (CVQKD) is the sharing of secret keys between different parties using the continuous amplitude and phase quadratures of light. There are many protocols in which different modulation schemes are used to implement CVQKD. However, there has been no tool for comparison between different CVQKD protocols to determine the optimal protocol for varying channels while simultaneously taking into account the effects of different parameters. Here, a comparison tool has been developed to map regions of positive secret key rate (SKR), given a channel's transmittance and excess noise, where a user's modulation can be adjusted to guarantee a positive SKR in an arbitrary environment. The method has been developed for discrete modulated CVQKD (DM-CVQKD) protocols but can be extended to other current and future protocols and security proofs.

quant-ph↗

arXiv2023

Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem from the viewpoint of quantum metrology, we are able to find optimal measurements under the assumption of good prior knowledge. We implement these measurements on a superconducting quantum computer. Our experiment produces sufficiently low error to allow the saturation of the theoretical limits, given by the Nagaoka--Hayashi bound. We also present simulations of adaptive measurement schemes utilizing the proposed method. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.

quant-ph↗

arXiv2023

Testing the postulates of quantum mechanics with coherent states of light and homodyne detection

Quantum mechanics has withstood every experimental test thus far. However, it relies on ad-hoc postulates which require experimental verification. Over the past decade there has been a great deal of research testing these postulates, with numerous tests of Born's rule for determining probabilities and the complex nature of the Hilbert space being carried out. Although these tests are yet to reveal any significant deviation from textbook quantum theory, it remains important to conduct such tests in different configurations and using different quantum states. Here we perform the first such test using coherent states of light in a three-arm interferometer combined with homodyne detection. Our proposed configuration requires additional assumptions, but allows us to use quantum states which exist in a larger Hilbert space compared to previous tests. For testing Born's rule, we find that the third order interference is bounded to be $κ$ = 0.002 $\pm$ 0.004 and for testing whether quantum mechanics is complex or not we find a Peres parameter of F = 1.0000 $\pm$ 0.0003 (F = 1 corresponds to the expected complex quantum mechanics). We also use our experiment to test Glauber's theory of optical coherence.

quant-ph↗

arXiv2023

Multiparameter estimation with two qubit probes in noisy channels

This work compares the performance of single and two qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel and the phase damping channel. For each channel we find the optimal single and two qubit probes. Where possible we demonstrate an explicit measurement strategy which saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two qubit probes show enhanced parameter estimation capabilities over single qubit probes for almost all non-identity channels, i.e. the achievable precision with a single qubit probe degrades faster with increasing exposure to the noisy environment than that of the two qubit probe. However, in sufficiently noisy channels, we show that it is possible for single qubit probes to outperform maximally entangled two qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-style nature of this paper will make it easily accessible.

quant-ph↗

arXiv2023

On the equivalence between squeezing and entanglement potential for two-mode Gaussian states

The maximum amount of entanglement achievable under passive transformations by continuous-variable states is called the entanglement potential. Recent work has demonstrated that the entanglement potential is upper-bounded by a simple function of the squeezing of formation, and that certain classes of two-mode Gaussian states can indeed saturate this bound, though saturability in the general case remains an open problem. In this study, we introduce a larger class of states that we prove saturates the bound, and we conjecture that all two-mode Gaussian states can be passively transformed into this class, meaning that for all two-mode Gaussian states, entanglement potential is equivalent to squeezing of formation. We provide an explicit algorithm for the passive transformations and perform extensive numerical testing of our claim, which seeks to unite the resource theories of two characteristic quantum properties of continuous-variable systems.

quant-ph↗

arXiv2023

Approaching optimal entangling collective measurements on quantum computing platforms

Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer better sensitivity, per resource, than what can be achieved classically. However, to reach the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks, collective measurements, which generate entanglement between multiple copies of the quantum state, are necessary. Here, we experimentally demonstrate theoretically optimal single- and two-copy collective measurements for simultaneously estimating two non-commuting qubit rotations. This allows us to implement quantum-enhanced sensing, for which the metrological gain persists for high levels of decoherence, and to draw fundamental insights about the interpretation of the uncertainty principle. We implement our optimal measurements on superconducting, trapped-ion and photonic systems, providing an indication of how future quantum-enhanced sensing networks may look.

quant-ph↗

arXiv2023

Satellite-to-Ground Continuous Variable Quantum Key Distribution: The Gaussian and Discrete Modulated Protocols in Low Earth Orbit

The Gaussian modulated continuous variable quantum key distribution (GM-CVQKD) protocol is known to maximise the mutual information between two parties during quantum key distribution (QKD). An alternative modulation scheme is the discrete modulated CVQKD (DM-CVQKD) protocol. In this paper, we study the Phase Shift Keying (M-PSK) and Quadrature Amplitude Modulation (M QAM) DM-CVQKD protocols along with the GM-CVQKD protocol over a satellite-to-ground link in the low SNR regime. We use a satellite-to-ground link model which takes into account geometric losses, scintillation, and scattering losses from the link distance, atmospheric turbulence, and atmospheric aerosols, respectively. In addition, recent multidimensional (MD) and multilevel coding and multistage decoding (MLC-MSD) reconciliation method models in combination with multiedge-type low-density parity-check (MET-LDPC) code models have been used to determine the reconciliation efficiency. The results show that GM-CVQKD outperforms DM-CVQKD. In addition, GM-CVQKD with MD reconciliation outperforms GM-CVQKD with MLC-MSD reconciliation in the finite size limit by producing positive secret key rates at larger link distances and lower elevation angles.

quant-ph↗