arXiv subjects

M. D. Reid

Publications and source records attributed to M. D. Reid.

At least 19 recordsLinked to original sources

arXiv2026

Physical currents for stochastic Einstein-Podolsky-Rosen quantum trajectories

Theories of the measured homodyne current generated by a stochastic Schrödinger equation (SSE) can be tested in a simulation of the Einstein-Podolsky-Rosen (EPR) correlations for a two-mode squeezed state. We carry out such a simulation, and determine the correct stochastic term for the measured current in the broad-band limit. Stratonovich rather than Ito stochastic noise agrees with experiment. We show that this is relevant to measurement noise and errors in quantum technologies. By analyzing the SSE trajectories as measurement settings are changed, we propose a modern version of Schrodinger's gedanken experiment, where one measures position and momenta simultaneously, ``one by direct, the other by indirect measurement''.

quant-ph↗

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↗

arXiv2024

Hidden causal loops, macroscopic realism and Einstein-Podolsky-Rosen-Bell nonlocality: forward-backward stochastic simulations

We analyze quantum measurement and entanglement by solving the dynamics of stochastic amplitudes that propagate both forward and backward in time. The model allows simulation of Einstein-Podolsky-Rosen and Bell correlations, and reveals consistency with a weak form of local realism defined after the unitary interactions determining the measurement settings. Bell violations emerge due to a breakdown of a subset of Bell's local-realism conditions. Our results elucidate how hidden causal loops can explain Bell nonlocality, without requiring retrocausality at a macroscopic level.

quant-ph↗

arXiv2023

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 $S_θ$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations $U_θ$ determining the measurement settings $θ$ 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 $S_θ$ distinguishing between the states. Deterministic macroscopic realism (dMR) posits MR for the system prior to the interaction $U_θ$. Weak macroscopic realism (wMR) posits MR for the system after $U_θ$, at the time $t_f$ (when the system is prepared for a final "pointer" measurement), the outcome of $S_θ$ not being changed by interactions that might occur at a remote system $B$. The premise also posits that if the outcome for $S_θ^A$ 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 $S_θ^A$ 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 Schrödinger, 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↗

arXiv2023

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↗

arXiv2023

A macroscopic quantum three-box paradox: finding consistency with weak macroscopic realism

The quantum three-box paradox considers a ball prepared in a superposition of being in one of three Boxes. Bob makes measurements by opening either Box 1 or Box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening Box 3. The paradox is that the ball would have been found with certainty in either box, if that box had been opened. Resolutions of the paradox include that Bob's measurement cannot be made non-invasively, or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument, by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes, prior to Bob or Alice opening any boxes. We demonstrate consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any Boxes, but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations, and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: The paradox only manifests if Alice's shuffling combines both local operations (on Box 3) and nonlocal operations, on the other Boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett-Garg inequality, which implies non-invasive measurability, if wMR holds.

quant-ph↗

arXiv2022

Wigner's Friend paradoxes: consistency with weak-contextual and weak-macroscopic realism models

Wigner's friend paradoxes highlight contradictions between measurements made by Friends inside a laboratory and superobservers outside a laboratory, who have access to an entangled state of the measurement apparatus. The contradictions lead to no-go theorems for observer-independent facts, thus challenging concepts of objectivity. Here, we examine the paradoxes from the perspective of establishing consistency with macroscopic realism. We present versions of the Brukner-Wigner-friend and Frauchiger-Renner paradoxes in which the spin-$1/2$ system measured by the Friends corresponds to two macroscopically distinct states. The local unitary operations $U_θ$ that determine the measurement setting $θ$ are carried out using nonlinear interactions, thereby ensuring measurements need only distinguish between the macroscopically distinct states. The macroscopic paradoxes are perplexing, seemingly suggesting there is no objectivity in a macroscopic limit. However, we demonstrate consistency with a contextual weak form of macroscopic realism (wMR): The premise wMR asserts that the system can be considered to have a definite spin outcome $λ_θ$, at the time after the system has undergone the unitary rotation $U_θ$ to prepare it in a suitable pointer basis. We further show that the paradoxical outcomes imply failure of deterministic macroscopic local realism, and arise when there are unitary interactions $U_θ$ occurring due to a change of measurement setting at both sites, with respect to the state prepared by each Friend. In models which validate wMR, there is a breakdown of a subset of the assumptions that constitute the Bell-Locality premise. A similar interpretation involving a weak contextual form of realism exists for the original paradoxes.

quant-ph↗

arXiv2022

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

Macroscopic delayed-choice and retrocausality: quantum eraser, Leggett-Garg and dimension witness tests with cat states

We propose delayed choice experiments carried out with macroscopic qubits, realised as macroscopically-distinct coherent states $|α\rangle$ and $|-α\rangle$. Quantum superpositions of $|α\rangle$ and $|-α\rangle$ are created via a unitary interaction $U(θ)$ based on a nonlinear Hamiltonian. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality (MrC). We therefore consider weak macroscopic realism (wMR), which specifies a hidden variable $λ_θ$ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting $ϕ$. Using entangled states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by $λ_θ$ without specification of the state at the level of $\hbar$, where fringes manifest. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the dimension witness inequality applied to the Wheeler-Chaves-Lemos-Pienaar experiment, where measurements need only distinguish the macroscopic qubit states. This negates all two-dimensional non-retrocausal models, thereby suggesting MrC. However, one can interpret consistently with wMR, thus avoiding MrC, by noting extra dimensions, and by noting that the violations require further unitary dynamics $U$ for each system. The violations are then explained as failure of deterministic macroscopic realism (dMR), which specifies validity of $λ_θ$ prior to the dynamics $U(θ)$ determining the measurement setting $θ$. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate EPR paradoxes at a microscopic level.

quant-ph↗

arXiv2021

Bipartite Leggett-Garg and macroscopic Bell inequality violations using cat states: distinguishing weak and deterministic macroscopic realism

We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin $1/2$ eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states (cat states). In this mapping, the unitary rotation of the Stern-Gerlach analyzer is realized by an interaction $H=Ω\hat{n}^{4}$ where $\hat{n}$ is the number of quanta. By adjusting the time of interaction, one alters the measurement setting. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements $\hat{M}$ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between subtly different definitions of macroscopic realism. Deterministic macroscopic local realism (dMR) assumes a definite outcome for the measurement $\hat{M}$ prior to the unitary rotation created by the analyser, and is negated by the violations. Weak macroscopic realism (wMR) assumes a definite outcome for systems prepared in a superposition $ψ_{pointer}$ of two macroscopically-distinct eigenstates of $\hat{M}$, after the unitary rotation. We find that wMR can be viewed as consistent with the violations. A model is presented, in which wMR holds, and for which the macroscopic violations emerge over the course of the unitary dynamics. Finally, we point out an EPR-type paradox, that a weak macro-realistic description for the system prior to the measurement $\hat{M}$ is inconsistent with the completeness of quantum mechanics.

quant-ph↗

arXiv2020

Dynamics of transient cat-states in degenerate parametric oscillation with and without nonlinear Kerr interactions

A cat-state is formed as the steady-state solution for the signal mode of an ideal, degenerate parametric oscillator, in the limit of negligible single-photon signal loss. In the presence of the signal loss, this is no longer true over timescales much longer than the damping time. However, for sufficient parametric nonlinearity, a cat-state can exist as a transient state. In this paper, we study the dynamics of the creation and decoherence of cat-states in degenerate parametric oscillation, both with and without the effect of a Kerr nonlinearity that applies to recent superconducting-circuit experiments generating cat-states in microwave cavities. We determine the time of formation and the lifetime of a cat-state in terms of three dimensionless parameters $λ$, $g$ and $χ$. These relate to the driving strength, the parametric nonlinearity, and the Kerr nonlinearity, respectively. We find that the Kerr nonlinearity has little effect on the threshold parametric nonlinearity ($g>1$) required for the formation of cat-states, and does not significantly alter the decoherence time of the cat-state, but can reduce the time of formation. The quality of the cat-state increases with the value $g$, and can also improved by the Kerr nonlinearity. To verify the existence and quality of the cat-state, we consider several signatures, including interference fringes and negativity, and show how they can be computed. We simulate a superconducting-circuit experiment using published experimental parameters and found good agreement with experimental results, indicating that a nonclassical cat-like state with a small Wigner negativity is generated in the experiment. A stronger nonlinearity would lead to a cat-state with convincing cat-state signatures. Finally, we explore the feasibility of creating large cat-states with a coherent amplitude of 20, corresponding to 400 photons.

quant-ph↗

arXiv2020

Criteria to detect genuine multipartite entanglement using spin measurements

We derive conditions in the form of inequalities to detect the genuine $N$-partite entanglement of $N$ systems. The inequalities are expressed in terms of variances of spin operators, and can be tested by local spin measurements performed on the individual systems. Violation of the inequalities is sufficient (but not necessary) to certify the multipartite entanglement, and occurs when a type of spin squeezing is created. The inequalities are similar to those derived for continuous-variable systems, but instead are based on the Heisenberg spin-uncertainty relation $ΔJ_{x}ΔJ_{y}\geq|\langle J_{z}\rangle|/2$. We also extend previous work to derive spin-variance inequalities that certify the full tripartite inseparability or genuine multi-partite entanglement among systems with fixed spin $J$, as in Greenberger-Horne-Zeilinger (GHZ) states and W states where $J=1/2$. These inequalities are derived from the planar spin-uncertainty relation $(ΔJ_{x})^{2}+(ΔJ_{y})^{2}\geq C_{J}$ where $C_{J}$ is a constant for each $J$. Finally, it is shown how the inequalities detect multipartite entanglement based on Stokes operators. We illustrate with experiments that create entanglement shared among separated atomic ensembles, polarization-entangled optical modes, and the clouds of atoms of an expanding spin-squeezed Bose-Einstein condensate. For each example, we give a criterion to certify the mutual entanglement.

quant-ph↗

arXiv2020

Overcoming decoherence of cat-states formed in a cavity using squeezed-state inputs

A cat-state is a superposition of two coherent states with amplitudes $α_{0}$ and $-α_{0}$. Recent experiments create cat states in a microwave cavity field using superconducting circuits. As with degenerate parametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the states are formed in a signal cavity mode via a two-photon dissipative process induced by the down conversion of a pump field to generate pairs of signal photons. The damping of the signal and the presence of thermal fluctuations rapidly decoheres the state, and the effect on the dynamics is to either destroy the possibility of a cat state, or else to sharply reduce the lifetime and size of the cat-states that can be formed. In this paper, we study the effect on both the DPO and microwave systems of a squeezed reservoir coupled to the cavity. While the threshold nonlinearity is not altered, we show that the use of squeezed states significantly lengthens the lifetime of the cat states. This improves the feasibility of generating cat states of large amplitude and with a greater degree of quantum macroscopic coherence, which is necessary for many quantum technology applications. Using current experimental parameters for the microwave set-up, which requires a modified Hamiltonian, we further demonstrate how squeezed states enhance the quality of the cat states that could be formed in this regime. Squeezing also combats the significant decoherence due to thermal noise, which is relevant for microwave fields at finite temperature. By modeling a thermal squeezed reservoir, we show that the thermal decoherence of the dynamical cat states can be inhibited by a careful control of the squeezing of the reservoir. To signify the quality of the cat state, we consider different signatures including fringes and negativity, and the $C_{l_{1}}$ measure of quantum coherence.

quant-ph↗

arXiv2020

Testing macroscopic local realism using cat-states and Bell inequalities in time

We show how one may test macroscopic local realism where, different from conventional Bell tests, all relevant measurements need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinguishable outcomes for a system observable and do not resolve microscopic properties (of order $\hbar$). Macroscopic local realism assumes: (1) macroscopic realism (the system prior to measurement is in a state which will lead to just one of the macroscopically distinguishable outcomes) and (2) macroscopic locality (a measurement on a system at one location cannot affect the macroscopic outcome of the measurement on a system at another location, if the measurement events are spacelike separated). To obtain a quantifiable test, we define $M$-scopic local realism where the outcomes are separated by an amount $\sim M$. We first show for $N$ up to $20$ that $N$-scopic Bell violations are predicted for entangled superpositions of $N$ bosons (at each of two sites). Secondly, we show violation of $M$-scopic local realism for entangled superpositions of coherent states of amplitude $α$, for arbitrarily large $M=α$. In both cases, the systems evolve dynamically according to a local nonlinear interaction. The first uses nonlinear beam splitters realised through nonlinear Josephson interactions; the second is based on nonlinear Kerr interactions. To achieve the Bell violations, the traditional choice between two spin measurement settings is replaced by a choice between different times of evolution at each site.

quant-ph↗

arXiv2019

Mesoscopic two-mode entangled and steerable states of 40,000 atoms in a Bose-Einstein condensate interferometer

Using criteria based on superselection rules, we analyze the quantum correlations between the two condensate modes of the Bose-Einstein condensate interferometer of Egorov et al. [Phys. Rev. A 84, 021605 (2011)]. In order to determine the two-mode correlations, we develop a multi-mode theory that describes the dynamics of the condensate atoms and the thermal fraction through the interferometer sequence, in agreement with the experimentally measured fringe visibility. We thus present experimental evidence for two-mode entangled states genuinely involving 40,000 ^{87}Rb atoms, and for two-way steerability between two groups of 20,000 indistinguishable atoms.

quant-ph↗

arXiv2019

Quantifying the mesoscopic nature of the Einstein-Podolsky-Rosen nonlocality

Evidence for Bell's nonlocality is so far mainly restricted to microscopic systems, where the elements of reality that are negated predetermine results of measurements to within one spin unit. Any observed nonlocal effect (or lack of classical predetermination) is then limited to no more than the difference of a single photon or electron being detected or not (at a given detector). In this paper, we analyze experiments that report Einstein-Podolsky-Rosen (EPR) steering form of nonlocality for mesoscopic photonic or Bose-Einstein condensate (BEC) systems. Using an EPR steering parameter, we show how the EPR nonlocalities involved can be quantified for four-mode states, to give evidence of nonlocal effects corresponding to a two-mode number difference of $10^{5}$ photons, or of several tens of atoms (at a given site). We also show how the variance criterion of Duan-Giedke-Cirac and Zoller for EPR entanglement can be used to determine a lower bound on the number of particles in a pure two-mode EPR entangled or steerable state, and apply to experiments.

quant-ph↗

arXiv2018

Creation, storage and retrieval of an optomechanical cat state

We analyze a method for the creation, storage and retrieval of optomechanical Schrodinger cat states, in which there is a quantum superposition of two distinct macroscopic states of a mechanical oscillator. In the proposal, an optical cat state is first prepared in an optical cavity, then transferred to the mechanical mode, where it is stored and later retrieved using control fields. We carry out numerical simulations for the quantum memory protocol for optomechanical cat states using the positive-P phase space representation. This has a compact, positive representation for a cat state, thus allowing a probabilistic simulation of this highly non-classical quantum system. To verify the effectiveness of the cat-state quantum memory, we consider several cat-state signatures and show how they can be computed. We also investigate the effects of decoherence on a cat state by solving the standard master equation for a simplified model analytically, allowing us to compare with the numerical results. Focusing on the negativity of the Wigner function as a signature of the cat state, we evaluate analytically an upper bound on the time taken for the negativity to vanish, for a given temperature of the environment of the mechanical oscillator. We show consistency with the numerical methods. These provide exact solutions, allowing a full treatment of decoherence in an experiment that involves creating, storing and retrieving mechanical cat states using temporally mode-matched input and output pulses. Our analysis treats the internal optical and mechanical modes of an optomechanical oscillator, and the complete set of input and output field modes which become entangled with the internal modes. The model includes decoherence due to thermal effects in the mechanical reservoirs, as well as optical and mechanical losses.

quant-ph↗

arXiv2018

Quantum software for linear photonic simulations

The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples, with experimental demonstrations and potential for obtaining a quantum computer to solve problems believed classically impossible. This introduces a challenge: how does one design or understand such photonic networks? We develop novel complex phase-space software for simulating these photonic networks, and apply this to boson sampling experiments. Our techniques give sampling errors orders of magnitude lower than experimental measurements of correlations, for the same number of samples. We show that these techniques remove systematic errors in previous algorithms for estimating correlations, with order of magnitude improvements in errors in some cases. In addition to that, we obtain a scalable channel-combination strategy for assessment of boson sampling devices.

quant-ph↗