arXiv subjects

Kiarn T. Laverick

Publications and source records attributed to Kiarn T. Laverick.

18 recordsLinked to original sources

arXiv2026

Optimizing Wigner Negativity in Scattering Processes Using Energetic Cost Functions

Wigner negativity is a key resource for quantum technologies but is difficult to optimize in multimode scattering systems. We study the scattering of coherent pulses by a two-level emitter coupled to a one-dimensional waveguide and introduce energetic cost functions that enable the optimization of Wigner negativity without reconstructing the full Wigner function. By decomposing the scattered energy into coherent, thermal, squeezing, and non-Gaussian contributions, we identify an energetic witness that strongly correlates with the achievable negativity across all driving regimes. This approach singles out optimal output temporal modes and uncovers operating points generating appreciable Wigner negativity with sub-photon input energies. We further identify a maximal energy-efficiency regime at spectral mode matching, where the emitter effectively implements a vacuum-selective $π$ phase shift, realizing a giant optical nonlinearity. These results establish energetic optimization as a practical route to engineering Wigner-negative photonic states in waveguide quantum electrodynamics and related bosonic scattering platforms.

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arXiv2026

Industry-ready spin-photon interfaces for hybrid photonic quantum computing

Hybrid photonic quantum computers, combining stationary matter qubits and flying photonic qubits, offer an intrinsically networked and resource-efficient route to large-scale, error-corrected quantum computation. Their core components are cavity-coupled matter qubits that act as light--matter interfaces, enabling: high-efficiency on-demand single-photon generation, stable near-unity photon indistinguishability and spin--multi-photon entanglement. Semiconductor quantum dots in microcavities are a leading platform for realizing such devices. Yet reaching the performance, reproducibility and spin-coherence thresholds for large-scale error correction remains a major challenge requiring industrial fabrication and control. Here we report thousands of monolithic semiconductor quantum-dot devices fabricated using a III--V pilot production-line process compatible with large-scale deployment. Systematic control of source parameters yields state-of-the-art efficiency and supports a path to optical losses below fault-tolerance thresholds. Using field-quadrature state reconstruction as a stringent joint test of efficiency and indistinguishability, we observe near-unity photon quantum purity stable over tens of minutes and a record single-photon Wigner-function negativity. We further demonstrate seven-partite spin--multi-photon entanglement and spin coherence extendable to microsecond timescales in the low-magnetic-field regime. Finally, photons from distant sources are as indistinguishable as photons emitted successively by a single source. These results establish foundry-compatible III--V quantum dots as a scalable platform for hybrid photonic quantum computing.

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arXiv2026

Energetics of non-Gaussianity in single mode cavities

Non-Gaussian states play a central role in quantum technologies, making the ability to quantify non-Gaussianity essential. We introduce an energetic framework to characterize non-Gaussianity in single-mode bosonic states by decomposing the total energy into Gaussian and non-Gaussian contributions. For pure states, we show that the non-Gaussian component defines a valid measure of non-Gaussianity and establish its connection to the relative entropy of non-Gaussianity. As an illustration, we compare this measure with Wigner negativity and find that both are maximized in closely related parameter regimes. For mixed states, we demonstrate that the non-Gaussian contribution acts as a faithful witness of non-Gaussianity. Our results reveal an energetic fine structure underlying non-Gaussianity and may provide practical insights for the efficient generation of non-Gaussian states.

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arXiv2026

Counterfactual quantum measurements

Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates counterfactuals using a hierarchy of desiderata. These were, however, built upon a deterministic classical framework, and whether it could be generalized to indeterministic quantum theory has been an open question. In this paper, we propose a formalism for quantum counterfactuals in which antecedents are measurement settings. Unlike other approaches, it non-trivially answers questions like: "Given that a photon-detector, observing an atom's fluorescence, clicked at a certain time, what would a field-quadrature detector have measured, if it had been used instead?"

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arXiv2026

An Energetic Constraint for Qubit-Qubit Entanglement

We analyze qubit-qubit entanglement from an energetic perspective and reveal an energetic trade-off between quantum coherence and entanglement. We decompose each qubit internal energy into a coherent and an incoherent component. The qubits' coherent energies are maximal if the qubit-qubit state is pure and separable. They decrease as qubit-qubit entanglement builds up under locally-energy-preserving processes. This yields a ``coherent energy deficit'' that we show is proportional to a well-known measure of entanglement, the square concurrence. In general, a qubit-qubit state can always be represented as a mixture of pure states. Then, the coherent energy deficit splits into a quantum component, corresponding to the average square concurrence of the pure states, and a classical one reflecting the mixedness of the joint state. Minimizing the quantum deficit over the possible pure state decompositions yields the square concurrence of the mixture. Our findings bring out new figures of merit to optimize and secure entanglement generation and distribution under energetic constraints.

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arXiv2025

Post-processed estimation of quantum state trajectories

Weak quantum measurements enable real-time tracking and control of dynamical quantum systems, producing quantum trajectories -- evolutions of the quantum state of the system conditioned on measurement outcomes. For classical systems, the accuracy of trajectories can be improved by incorporating future information, a procedure known as smoothing. Here we apply this concept to quantum systems, generalising a formalism of quantum state smoothing for an observer monitoring a quantum system exposed to environmental decoherence, a scenario important for many quantum information protocols. This allows future data to be incorporated when reconstructing the trajectories of quantum states. We experimentally demonstrate that smoothing improves accuracy using a continuously measured nanomechanical resonator, showing that the method compensates for both gaps in the measurement record and inaccessible environments. We further observe a key predicted departure from classical smoothing: quantum noise renders the trajectories nondifferentiable. These results establish that future information can enhance quantum trajectory reconstruction, with potential applications across quantum sensing, control, and error correction.

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arXiv2025

Quantum State Smoothing for Linear Gaussian Systems

Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified for Linear Gaussian quantum systems, which have wide physical applicability. We derive a closed-form solution for the quantum smoothed state, which is more pure than the standard filtered state, whilst still being described by a physical quantum state, unlike other proposed quantum smoothing techniques. We apply the theory to an on-threshold optical parametric oscillator, exploring optimal conditions for purity recovery by smoothing. The role of quantum efficiency is elucidated, in both low and high efficiency limits.

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arXiv2025

Tracking Quantum Dynamics in an Optical Cavity for Recovering Purity and Squeezing via Quantum State Smoothing

Tracking the dynamics of a quantum system is conventionally achieved by monitoring the system continuously in time and filtering the information contained in measurement records via the causal quantum trajectory approach. However, in practical scenarios there is often loss of information to the environment, leading to filtered states that are impure because of decoherence. If real-time tracking is not required, the lost information can be maximally extracted via acausal quantum state smoothing, which has been theoretically proven to better restore the system's coherence (purity) than causal filtering. Interestingly, quantum state smoothing requires assumptions of how any lost quantum information (unobserved by the experimenter) was turned into classical information by the environment. In this work, we experimentally demonstrate smoothing scenarios, using an optical parametric oscillator and introducing `observed' and `unobserved' channels by splitting the output beam into two independent homodyne detectors. We achieve improvement in state purification of 10.3% +/- 1.6%, squeezing restoration of 7.6% +/- 2.6%, and show that smoothed states are better estimates of hidden true states than those from conventional filtering. The estimation techniques used in this paper are promising for many applications in quantum information that incorporate post-processing.

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arXiv2025

Linear Gaussian Quantum State Smoothing: Understanding the optimal unravelings for Alice to estimate Bob's state

Quantum state smoothing is a technique to construct an estimate of the quantum state at a particular time, conditioned on a measurement record from both before and after that time. The technique assumes that an observer, Alice, monitors part of the environment of a quantum system and that the remaining part of the environment, unobserved by Alice, is measured by a secondary observer, Bob, who may have a choice in how he monitors it. The effect of Bob's measurement choice on the effectiveness of Alice's smoothing has been studied in a number of recent papers. Here we expand upon the Letter which introduced linear Gaussian quantum (LGQ) state smoothing [Phys. Rev. Lett., 122, 190402 (2019)]. In the current paper we provide a more detailed derivation of the LGQ smoothing equations and address an open question about Bob's optimal measurement strategy. Specifically, we develop a simple hypothesis that allows one to approximate the optimal measurement choice for Bob given Alice's measurement choice. By 'optimal choice' we mean the choice for Bob that will maximize the purity improvement of Alice's smoothed state compared to her filtered state (an estimated state based only on Alice's past measurement record). The hypothesis, that Bob should choose his measurement so that he observes the back-action on the system from Alice's measurement, seems contrary to one's intuition about quantum state smoothing. Nevertheless we show that it works even beyond a linear Gaussian setting.

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arXiv2025

Inequivalent ways to apply semi-classical smoothing to a quantum system

In this paper, we correct a mistake we made in [Phys. Rev. Lett. $\textbf{122}$, 190402 (2019)] and [Phys. Rev. A $\textbf{103}$, 012213 (2021)] regarding the Wigner function of the so-called smoothed Weak-Valued state (SWV state). Here smoothing refers to estimation of properties at time $t$ using information obtained in measurements both before and after $t$. The SWV state is a pseudo-state (Hermitian but not necessarily positive) that gives, by the usual trace formula, the correct value for a weak measurement preformed at time $t$, $\textit{i.e.}$, its weak value. The Wigner function is a pseudo-probability-distribution (real but not necessarily positive) over phase-space. A smoothed (in this estimation sense) Wigner distribution at time $t$ can also be defined by applying classical smoothing for probability-distributions to the Wigner functions. The smoothed Wigner distribution (SWD) gives identical means for the canonical phase-space variables as does the SWV state. However, contrary to the assumption in the above references, the Wigner function of the SWV state is not the smoothed Wigner distribution.

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arXiv2025

Quantum state smoothing when Alice assumes the wrong type of monitoring by Bob

An open quantum system leaks information into its environment. In some circumstances it is possible for an observer, say Alice, to recover that information, as a classical measurement record, in a variety of different ways, using different experimental setups. The optimal way for Alice to estimate the quantum state at time $t$ from the record before $t$ is known as quantum filtering. Recently, a version of quantum smoothing, in which Alice estimates the state at time $t$ using her record on both sides of $t$, has been developed. It requires Alice to make optimal inferences about the pre-$t$ record of a second observer, say Bob, who recovers whatever information Alice does not. But for Alice to make this inference, she needs to know Bob's setup. In this paper we consider what happens if Alice is mistaken in her assumption about Bob's setup. We show that the accuracy -- as measured by the Trace-Squared-Deviation, of Alice's estimate of the true state (i.e., the state conditioned on her and Bob's pre-$t$ records) -- depends strongly on her setup, Bob's actual setup, and the wrongly assumed setup. Using resonance fluorescence as a model system, we show numerically that in some cases the wrong smoothing is almost as accurate as the right smoothing, but in other cases much less accurate, even being less accurate than Alice's filtered estimate. Curiously, in some of the latter cases the fidelity of Alice's wrong estimate with the true state is actually higher than that of her right estimate. We explain this, and other features we observe numerically, by some simple analytical arguments.

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arXiv2025

A Retrodictive Approach to Quantum State Smoothing

Smoothing is a technique for estimating the state of an imperfectly monitored open system by combining both prior and posterior measurement information. In the quantum regime, current approaches to smoothing either give unphysical outcomes, due to the non-commutativity of the measurements at different times, or require assumptions about how the environment is measuring the system, which with current technology is unverifiable. We propose a novel definition of the smoothed quantum state based on quantum Bayesian retrodiction, which mirrors the classical retrodictive approach to smoothing. This approach always yields physical results and does not require any assumption on the environment. We show that this smoothed state has, on average, greater purity than the state reconstructed using just the prior information. Finally, we make a connection with the smoothing theory of Guevara and Wiseman in a well-studied regime, and describe from a purely quantum perspective how it conditions on the posterior information.

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arXiv2023

Quantum state smoothing cannot be assumed classical even when the filtering and retrofiltering are classical

State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the $\textit{filtered state}$ (a state conditioned only on the past measurement information and the initial preparation) and the $\textit{retrofiltered effect}$ (depending only on the future measurement information). For the quantum case, whilst there are well-established analogues of the filtered state ($ρ_{\rm F}$) and retrofiltered effect ($\hat E_{\rm R}$), their product does not, in general, provide a valid quantum state for smoothing. However, this procedure does seem to work when $ρ_{\rm F}$ and $\hat E_{\rm R}$ are mutually diagonalizable. This fact has been used to obtain smoothed quantum states -- more pure than the filtered states -- in a number of experiments on continuously monitored quantum systems, in cavity QED and atomic systems. In this paper we show that there is an implicit assumption underlying this technique: that if all the information were known to the observer, the true system state would be one of the diagonal basis states. This assumption does not necessarily hold, as the missing information is quantum information. It could be known to the observer only if it were turned into a classical measurement record, but then its nature depends on the choice of measurement. We show by a simple model that, depending on that measurement choice, the smoothed quantum state can: agree with that from the classical method; disagree with it but still be co-diagonal with it; or not even be co-diagonal with it. That is, just because filtering and retrofiltering appear classical does not mean classical smoothing theory is applicable in quantum experiments.

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arXiv2021

Unifying theory of quantum state estimation using past and future information

Quantum state estimation for continuously monitored dynamical systems involves assigning a quantum state to an individual system at some time, conditioned on the results of continuous observations. The quality of the estimation depends on how much observed information is used and on how optimality is defined for the estimate. In this work, we consider problems of quantum state estimation where some of the measurement records are not available, but where the available records come from both before (past) and after (future) the estimation time, enabling better estimates than is possible using the past information alone. Past-future information for quantum systems has been used in various ways in the literature, in particular, the quantum state smoothing, the most-likely path, and the two-state vector and related formalisms. To unify these seemingly unrelated approaches, we propose a framework for partially-observed quantum system with continuous monitoring, wherein the first two existing formalisms can be accommodated, with some generalization. The unifying framework is based on state estimation with expected cost minimization, where the cost can be defined either in the space of the unknown record or in the space of the unknown true state. Moreover, we connect all three existing approaches conceptually by defining five new cost functions, and thus new types of estimators, which bridge the gaps between them. We illustrate the applicability of our method by calculating all seven estimators we consider for the example of a driven two-level system dissipatively coupled to bosonic baths. Our theory also allows connections to classical state estimation, which create further conceptual links between our quantum state estimators.

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arXiv2021

Quantum state smoothing as an optimal estimation problem with three different cost functions

Quantum state smoothing is a technique to estimate an unknown true state of an open quantum system based on partial measurement information both prior and posterior to the time of interest. In this paper, we show that the smoothed quantum state is an optimal state estimator; that is, it minimizes a risk (expected cost) function. Specifically, we show that the smoothed quantum state is optimal with respect to two cost functions: the trace-square deviation from and the relative entropy to the unknown true state. However, when we consider a related risk function, the linear infidelity, we find, contrary to what one might expect, that the smoothed state is not optimal. For this case, we derive the optimal state estimator, which we call the lustrated smoothed state. It is a pure state, the eigenstate of the smoothed quantum state with the largest eigenvalue.

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arXiv2021

The Quantum Rauch-Tung-Striebel Smoothed State

Smoothing is a technique that estimates the state of a system using measurement information both prior and posterior to the estimation time. Two notable examples of this technique are the Rauch-Tung-Striebel and Mayne-Fraser-Potter smoothing techniques for linear Gaussian systems, both resulting in the optimal smoothed estimate of the state. However, when considering a quantum system, classical smoothing techniques can result in an estimate that is not a valid quantum state. Consequently, a different smoothing theory was developed explicitly for quantum systems. This theory has since been applied to the special case of linear Gaussian quantum (LGQ) systems, where, in deriving the LGQ state smoothing equations, the Mayne-Fraser-Potter technique was utilised. As a result, the final equations describing the smoothed state are closely related to the classical Mayne-Fraser-Potter smoothing equations. In this paper, I derive the equivalent Rauch-Tung-Striebel form of the quantum state smoothing equations, which further simplify the calculation for the smoothed quantum state in LGQ systems. Additionally, the new form of the LGQ smoothing equations bring to light a property of the smoothed quantum state that was hidden in the Mayne-Fraser-Potter form, the non-differentiablilty of the smoothed mean. By identifying the non-differentiable part of the smoothed mean, I was then able to derive a necessary and sufficient condition for the quantum smoothed mean to be differentiable in the steady state regime.

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arXiv2020

General criteria for quantum state smoothing with necessary and sufficient criteria for linear Gaussian quantum systems

Quantum state smoothing is a technique for estimating the quantum state of a partially observed quantum system at time $τ$, conditioned on an entire observed measurement record (both before and after $τ$). However, this smoothing technique requires an observer (Alice, say) to know the nature of the measurement records that are unknown to her in order to characterize the possible true states for Bob's (say) systems. If Alice makes an incorrect assumption about the set of true states for Bob's system, she will obtain a smoothed state that is suboptimal, and, worse, may be unrealizable (not corresponding to a valid evolution for the true states) or even unphysical (not represented by a state matrix $ρ\geq0$). In this paper, we review the historical background to quantum state smoothing, and list general criteria a smoothed quantum state should satisfy. Then we derive, for the case of linear Gaussian quantum systems, a necessary and sufficient constraint for realizability on the covariance matrix of the true state. Naturally, a realizable covariance of the true state guarantees a smoothed state which is physical. It might be thought that any putative true covariance which gives a physical smoothed state would be a realizable true covariance, but we show explicitly that this is not so. This underlines the importance of the realizabilty constraint.

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arXiv2017

Adaptive estimation of a time-varying phase with coherent states: smoothing can give an unbounded improvement over filtering

The problem of measuring a time-varying phase, even when the statistics of the variation is known, is considerably harder than that of measuring a constant phase. In particular, the usual bounds on accuracy - such as the $1/(4\bar{n})$ standard quantum limit with coherent states - do not apply. Here, restricting to coherent states, we are able to analytically obtain the achievable accuracy - the equivalent of the standard quantum limit - for a wide class of phase variation. In particular, we consider the case where the phase has Gaussian statistics and a power-law spectrum equal to $κ^{p-1}/|ω|^p$ for large $ω$, for some $p>1$. For coherent states with mean photon flux ${\cal N}$, we give the Quantum Cramér-Rao Bound on the mean-square phase error as $[p \sin (π/p)]^{-1}(4{\cal N}/κ)^{-(p-1)/p}$. Next, we consider whether the bound can be achieved by an adaptive homodyne measurement, in the limit ${\cal N}/κ\gg 1$ which allows the photocurrent to be linearized. Applying the optimal filtering for the resultant linear Gaussian system, we find the same scaling with ${\cal N}$, but with a prefactor larger by a factor of $p$. By contrast, if we employ optimal smoothing we can exactly obtain the Quantum Cram{é}r-Rao Bound. That is, contrary to previously considered ($p=2$) cases of phase estimation, here the improvement offered by smoothing over filtering is not limited to a factor of 2 but rather can be unbounded by a factor of $p$. We also study numerically the performance of these estimators for an adaptive measurement in the limit where ${\cal N}/κ$ is not large, and find a more complicated picture.

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