arXiv subjects

Run Yan Teh

Publications and source records attributed to Run Yan Teh.

15 recordsLinked to original sources

arXiv2026

Q-based, objective-field model for wave-function collapse: Analyzing measurement on a macroscopic superposition state

In this paper, we examine measurement using the Q-based, objective-field model for quantum mechanics. Schrodinger considered a microscopic system prepared in a superposition of states which is then coupled to a macroscopic meter. We analyze the entangled meter and system, and measurements on it, by solving forward-backward stochastic differential equations for real amplitudes $x(t)$ and $p(t)$ that correspond to the phase-space variables of the Q function of the system at a time $t$. We model the system and meter as single-mode fields, and measurement of $\hat{x}$ by amplification of the amplitude $x(t)$. Our conclusion is that the outcome for the measurement is determined at (or by) the time $t_{m}$, when the coupling to the meter is complete, the meter states being macroscopically distinguishable. There is consistency with macroscopic realism. By evaluating the distribution of the amplitudes $x$ and $p$ postselected on a given outcome of the meter, we show how the $Q$-based model represents a more complete description of quantum mechanics: The variances associated with amplitudes $x$ and $p$ are too narrow to comply with the uncertainty principle, ruling out that the distribution represents a quantum state. We conclude that the collapse of the wavefunction occurs as a two-stage process: First there is an amplification that creates branches of amplitudes $x(t)$ of the meter, associated with distinct eigenvalues. The outcome of measurement is determined by $x(t)$ once amplified, explaining Born's rule. Second, the distribution that determines the final collapse is the state inferred for the system conditioned on the outcome of the meter: information is lost about the meter, in particular, about the complementary variable $p$.

quant-ph↗

arXiv2025

Non-periodic Fourier propagation algorithms for partial differential equations

Spectral methods for partial differential equations (PDEs) with non-periodic boundary conditions arising in computational physics often use polynomial expansions on non-uniform grids. Here, we implement a Fourier method that employs fast trigonometric expansions on a uniform grid with non-periodic boundaries using fast discrete sine transforms (DST) or/and discrete cosine transforms (DCT) to solve parabolic PDEs. We implement this method in two ways: either using a Fourier spectral derivative or a Fourier interaction picture. Both methods can treat vector fields with a combination of Dirichlet and/or Neumann boundary conditions in one or more space dimensions. As examples, we use them to solve a variety of computational physics PDEs with analytical solutions, including the Peregrine solitary wave solution. For the 1D heat equation problem, our method with an interaction picture is accurate up to machine precision. Soluble examples of stochastic partial differential equation (SPDE) with non-periodic boundaries in one and two space dimensions, with physics and interdisciplinary applications are also treated. We compare the results obtained from these algorithms with publicly available solvers that use polynomial spectral methods, and study their relative performance and error scaling. Polynomial methods with non-uniform spatial grids have lower spatial discretization errors when the solutions change slowly in space, typically with large spatial grids. For problems with rapid spatial variation, Fourier methods can outperform polynomial expansions, owing to their smaller maximum space interval, and are generally faster due to the computational efficiency of discrete Fourier transform methods. We verified this by making a complexity analysis in which we studied the total error at the optimum combination of time and space steps for a given resource use.

math.NA↗

arXiv2025

Quest for quantum advantage: Monte Carlo wave-function simulations of the Coherent Ising Machine

The Coherent Ising Machine (CIM) is a quantum network of optical parametric oscillators (OPOs) intended to find ground states of the Ising model. This is an NP-hard problem, related to several important minimization problems, including the max-cut graph problem. In order to enhance its potential performance, we analyze the coherent coupling strategy for the CIM in a highly quantum regime. To explore this limit, without assuming gaussianity, we employ accurate numerical simulations. Due to the inherent complexity of the system, the maximum network size is limited. While master equation methods can be used, their scalability diminishes rapidly for larger systems. Instead, we use Monte Carlo wave-function methods, which scale as the wave-function dimension, and use large numbers of samples. These simulations involve Hilbert spaces exceeding $10^{7}$ dimensions. To evaluate success probabilities, we use quadrature probabilities. We demonstrate the potential for quantum computational advantage by reducing the time required to reach maximum success probability in a low-dissipation regime enabled by initial quantum superpositions and entanglement. Furthermore, we demonstrate that tailored time-dependent couplings can amplify these quantum effects. Comparisons with classical CIM models give evidence that quantum tunneling effects in this strong coupling limit can overcome trapping in false minima. This can greatly increase success rates, indicating a potential for quantum advantage. Finally, we perform a coherence analysis based on the state purity to examine the role of quantum coherence in CIM performance and to determine how state purity correlates with improved optimization outcomes.

quant-ph↗

arXiv2024

Complexity order of multiple resource algorithms

Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random ensemble competes with the time-step. We define the complexity order of an algorithm needing multiple resources as the exponent of inverse total error with respect to the total resources used. The optimum order is predicted for independent, factorable resources. We show that it equals the inverse sum of the inverse resource orders. This is applied to computing averages in a stochastic differential equation. We treat numerical examples for multiple different algorithms and for stochastic partial differential equations, all giving quantitative results in excellent agreement with our more general analytic theory.

physics.comp-ph↗

arXiv2024

Sub-100-fs formation of dark excitons in monolayer WS2

Two-dimensional semiconducting transition metal dichalcogenides (TMDs) are promising for optoelectronic applications due to their strongly bound excitons. While bright excitons have been thoroughly scrutinized, dark excitons are much less investigated as they are not observable with far-field spectroscopy. However, with their non-zero momenta, dark excitons are significant for applications requiring long-range transport or coupling to external fields. We access such dark excitons in WS2 monolayer using transient photoemission electron microscopy with sub-diffraction limited spatial resolution (75 nm) and exceptionally high temporal resolution (13 fs). Image time series of TMD flakes are recorded at several different fluences. We directly observe the ultrafast formation of dark K-Q excitons in monolayer WS2 occurring within 14-50 fs and follow their subsequent picosecond decay. We distinguish exciton dynamics between the interior and edges of the monolayer TMD and conclude that the long-term evolution of dark excitations is defect-mediated while intervalley scattering is not affected.

cond-mat.mes-hall↗

arXiv2023

The Quantum and Stochastic Toolbox: xSPDE4.2

This is the fourth major release of the xSPDE toolbox, which solves stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. The equations can have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector component, and at either end of any interval. xSPDE has functions that can numerically solve both ordinary and partial differential stochastic equations of any type, obtaining correlations, probabilities and averages. The toolbox has a core treating stochastic differential equations, with averages, probability distributions and full error estimates. There are stochastic extensions treating applications to partial differential equations, projected equations, quantum stochastic equations, master equations and quantum phase-space simulations including Gaussian boson sampling experiments.

quant-ph↗

arXiv2022

An Einstein-Podolsky-Rosen argument based on weak forms of local realism not falsifiable by GHZ or Bell experiments

The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on the premises of local realism. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsifiable by these experiments. We propose macroscopic EPR and GHZ experiments using spins $S_\theta$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations $U_\theta$ determining the measurement settings $\theta$ are devices that create macroscopic superposition states. For a system with two macroscopically distinct states available, macroscopic realism (MR) posits a predetermined outcome for a measurement $S_\theta$ distinguishing between the states. Deterministic macroscopic realism (dMR) posits MR for the system prior to the interaction $U_\theta$. Weak macroscopic realism (wMR) posits MR for the system after $U_\theta$, at the time $t_f$ (when the system is prepared for a final "pointer" measurement), the outcome of $S_\theta$ not being changed by interactions that might occur at a remote system $B$. The premise also posits that if the outcome for $S_\theta^A$ of a system $A$ can be predicted by a pointer measurement on a system $B$ defined after the interaction fixing the setting at $B$, then the outcome for $S_\theta^A$ is determined at this time. The GHZ predictions negate dMR but are consistent with wMR. Yet, an EPR paradox arises based on wMR for the set-up proposed by Schr\"odinger, where one measures two complementary spins simultaneously, "one by direct, the other by indirect" measurement. We revisit the original EPR paradox and find similarly that an EPR argument can be based on a weak form of local realism not falsifiable by GHZ or Bell tests.

quant-ph↗

arXiv2021

Simulating macroscopic quantum correlations in linear networks

Many developing quantum technologies make use of quantum networks of different types. Even linear quantum networks are nontrivial, as the output photon distributions can be exponentially complex. Despite this, they can still be computationally simulated. The methods used are transformations into equivalent phase-space representations, which can then be treated probabilistically. This provides an exceptionally useful tool for the prediction and validation of experimental results, including decoherence. As well as experiments in Gaussian boson sampling, which are intended to demonstrate quantum computational advantage, these methods are applicable to other types of entangled linear quantum networks as well. This paper provides a tutorial and review of work in this area, to explain quantum phase-space techniques using the positive-P and Wigner distributions.

quant-ph↗

arXiv2021

Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems

This paper reviews the progress that has been made in our knowledge of quantum correlations at the mesoscopic and macroscopic level. We begin by summarizing the Einstein-Podolsky-Rosen (EPR) argument and the Bell correlations that cannot be explained by local hidden variable theories. It was originally an open question as to whether (and how) such quantum correlations could occur on a macroscopic scale, since this would seem to counter the correspondence principle. The purpose of this review is to examine how this question has been answered over the decades since the original papers of EPR and Bell. We first review work relating to higher spin measurements which revealed that macroscopic quantum states could exhibit Bell correlations. This covers higher dimensional, multi-particle and continuous-variable EPR and Bell states where measurements on a single system give a spectrum of outcomes, and also multipartite states where measurements are made at multiple separated sites. It appeared that the macroscopic quantum observations were for an increasingly limited span of measurement settings and required a fine resolution of outcomes. Motivated by this, we next review correlations for macroscopic superposition states, and examine predictions for the violation of Leggett-Garg inequalities for dynamical quantum systems. These results reveal Bell correlations for coarse-grained measurements which need only distinguish between macroscopically distinct states, thus bringing into question the validity of certain forms of macroscopic realism. Finally, we review progress for massive systems, including Bose-Einstein condensates and optomechanical oscillators, where EPR-type correlations have been observed between massive systems. Experiments are summarized, which support the predictions of quantum mechanics in mesoscopic regimes.

quant-ph↗

arXiv2021

Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems

We derive inequalities sufficient to detect the genuine $N$-partite steering of $N$ distinct systems. Here, we are careful to distinguish between the concepts of full $N$-partite steering inseparability (where steering is confirmed individually for all bipartitions of the $N$ systems, thus negating the bilocal hidden state model for each bipartition) and genuine $N$-partite steering (which excludes all convex combinations of the bilocal hidden state models). Other definitions of multipartite steering are possible and we derive inequalities to detect a stricter genuine $N$-partite steering based on only one trusted site. The inequalities are expressed as variances of quadrature phase amplitudes and thus apply to continuous variable systems. We show how genuine $N$-partite steerable states can be created and detected for the nodes of a network formed from a single-mode squeezed state passed through a sequence of $N-1$ beam splitters. A stronger genuine $N$-partite steering is created, if one uses two squeezed inputs, or $N$ squeezed inputs. We are able to confirm that genuine tripartite steering (by the above definition and the stricter definition) has been realised experimentally. Finally, we analyze how bipartite steering and entanglement is distributed among the systems in the tripartite case, illustrating with monogamy inequalities. While we use Gaussian states to benchmark the criteria, the inequalities derived in this paper are not based on the assumption of Gaussian states, which gives advantage for quantum communication protocols.

quant-ph↗

arXiv2021

Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality

Violation of Leggett-Garg inequalities allows proof of the incompatibility between quantum mechanics and the combined premises (called macrorealism) of macroscopic realism (MR) and non-invasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails $-$ or else, that NIM fails. In this paper, we consider a strong failure of macrorealism, involving superpositions of coherent states, where the NIM premise is replaced by Bell-locality. We follow recent work and propose validity of a subset of Einstein-Podolsky-Rosen (EPR) and Leggett-Garg premises, referred to as \emph{weak macroscopic realism} (wMR). In finding consistency with wMR, we identify that the Leggett-Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a less restrictive sense. Weak MR is distinguished from \emph{deterministic macroscopic realism} (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits a predetermined value for the measurement outcome, for the system defined at the time after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the element of reality defined by EPR for a system A, where one can predict with certainty the outcome of a measurement on A, by measurement on a system B. Weak MR posits that the element of reality exists once the unitary interaction determining the setting at B has occurred. We show compatibility of systems violating Leggett-Garg inequalities with wMR, but point out that dMR is falsifiable. We compare with other MR models, and give an argument for wMR on the basis that wMR resolves inconsistencies pointed out by Leggett and Garg between failure of macrorealism and assumptions intrinsic to quantum measurement theory.

quant-ph↗

arXiv2019

Discrete time symmetry breaking in quantum circuits: exact solutions and tunneling

We discuss general properties of discrete time quantum symmetry breaking in degenerate parametric oscillators. Recent experiments in superconducting quantum circuit with Josephson junction nonlinearities give rise to new properties of strong parametric coupling and nonlinearities. Exact analytic solutions are obtained for the steady-state of this single-mode case of subharmonic generation. We also obtain analytic solutions for the tunneling time over which the time symmetry-breaking is lost above threshold. We find that additional anharmonic terms found in the superconducting case increase the tunneling rate, and can also lead to new regimes of tristability as well as bistability. Our analytic results are confirmed by number state calculations.

quant-ph↗

arXiv2019

Schrödinger cats and steady states in subharmonic generation with Kerr nonlinearities

We discuss general properties of the equilibrium state of parametric down-conversion in superconducting quantum circuits with detunings and Kerr anharmonicities, in the strongly nonlinear regime. By comparing moments of the steady state and those of a Schrödinger cat, we show that true Schrödinger cats cannot survive in the steady state if there is any single-photon loss. A delta-function 'cat-like' steady-state distribution can be formed, but this only exists in the limit of an extremely large nonlinearity. The steady state is a mixed state, which is more complex than a mixture or linear combination of delta-functions, and whose purity is reduced by driving. We expect this general behaviour to occur in other driven, dissipative quantum subharmonic non-equilibrium open systems.

quant-ph↗

arXiv2018

Quantum fidelity measures for mixed states

Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories, quantum computers, quantum communications, and quantum phase-space simulations.

quant-ph↗

arXiv2014

Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks

The Einstein-Podolsky-Rosen (EPR) paradox established a link between entanglement and nonlocality in quantum mechanics. EPR steering is the nonlocality associated with the EPR paradox and has traditionally only been investigated between two parties. Here, we present the first experimental observations of multipartite EPR steering, and of the genuine tripartite continuous variable entanglement of three mesoscopic optical systems. We explore different linear optics networks - each one with optimised asymmetries - that create multipartite steerable states containing different numbers of quantised optical modes (qumodes). By introducing asymmetric loss on a 7-qumode state, we characterize 8 regimes of directional steering, showing that N + 1 regimes exist for an N-qumode state. Further, we reveal the directional monogamy of steering, and experimentally demonstrate continuous variable one-sided semi device-independent quantum secret sharing. Our methods establish principles for the development of multiparty quantum communication protocols with asymmetric observers, and can be extended to qubits, whether photonic, atomic, superconducting, or otherwise.

quant-ph↗