arXiv subjects

Howard M. Wiseman

Publications and source records attributed to Howard M. Wiseman.

At least 19 recordsLinked to original sources

arXiv2026

Cascading amplifiers can create exponentially large coherence

A standard laser beam has photon degeneracy, or coherence, $\mathfrak{C}$, of at most $8μ^2$, where $μ$ is the number of photons in the laser itself. Even quantum-engineered lasers, if required to produce a beam with the standard statistical properties, have limited coherence, scaling as $μ^4$. Moreover, such lasers (still unrealised) require very unconventional gain and output-coupling mechanisms. Here, we propose a different path to increasing $\mathfrak{C}$: cascaded linear amplifiers, with conventional couplings. By dropping the requirement on the beam's properties, this approach can, in theory, achieve $\mathfrak{C}$ scaling exponentially in $μ$. Here $μ$ is the total source excitation number, across all the amplifiers. Two amplifiers suffice to surpass the standard $μ^2$ scaling.

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arXiv2026

Multi-level Random-Telegraph Noise Mitigation using a Single Spectator Qubit

Preserving quantum coherence in the presence of environmental noise is one of the principal challenges for quantum technologies. Noise mitigation using spectator qubits (SQs) has recently emerged as a promising approach, enabling indirect probing of the noise without disturbing the data qubit (DQ). However, existing analyses that probe ultimate performance have been restricted to two-state random telegraph process noise, which does not capture more complex noise processes that may arise in the environment. Therefore, we here develop a SQ-based noise mitigation for DQs subject to general multi-level fluctuator noise. We first derive the coherence dynamics of the DQ under such noise, then develop a mitigation scheme in which information about the noise is inferred from sequential SQ measurements and used for phase correction. A memory-efficient heuristic adaptive protocol is proposed to dynamically select the SQ measurement time and angle based on the current noise estimate. Numerical simulations demonstrate that the proposed strategy significantly suppresses decoherence under multi-level noise, achieving performance comparable to that in the two-level case despite the increased complexity of the noise process.

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arXiv2026

Entropy Flow of a Laser Beam

A laser beam is often modelled by a pure coherent state. In fact its state is mixed, even if it has coherent-state photon-number statistics (Poissonian), because the phase must vary. We consider such an ideal laser beam, with phase diffusion rate $\ell$, equal to its (Lorentzian) spectral width. We show that the beam entropy is extensive, with an entropy flow of $\dot{S} = \kB\sqrt{\dot{N}\ell}$, where $\dot{N}$ is the number flow. We give an intuitive explanation for this remarkably simple result, and compare it to the entropy flow of a unidirectional thermal beam.

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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

Quantum trajectories for time-binned data and their closeness to fully conditioned quantum trajectories

Quantum trajectories are dynamical equations for quantum states conditioned on the results of a time-continuous measurement, such as a continuous-in-time current $\vec y_t$. Recently there has been renewed interest in dynamical maps for quantum trajectories with time-intervals of finite size $Δt$. Guilmin \emph{et al.} (unpublished) derived such a dynamical map for the (experimentally relevant) case where only the average current $I_t$ over each interval is available. Surprisingly, this binned data still generates a conditioned state $ρ_\text{\faFaucet}$ that is almost pure (for efficient measurements), with an impurity scaling as $(Δt)^{3}$. We show that, nevertheless, the typical distance of $ρ_\text{\faFaucet}$ from $\hatψ_{\text{F}; \vec y_t}$ -- the projector for the pure state conditioned on the full current -- is as large as $(Δt)^{3/2}$. We introduce another finite-interval dynamical map (``$Φ$-map''), which requires only one additional real statistic, $ϕ_t$, of the current in the interval, that gives a conditioned state $\hatψ_Φ$ which is only $(Δt)^{2}$-distant from $\hatψ_{\text{F}; \vec y_t}$. We numerically verify these scalings of the error (distance from the true states) for these two maps, as well as for the lowest-order (Itô) map and two other higher-order maps. Our results show that, for a generic system, if the statistic $ϕ_t$ can be extracted from experiment along with $I_t$, then the $Φ$-map gives a smaller error than any other.

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arXiv2026

Detection-loophole-free nonlocality in the simplest scenario

Loophole-free quantum nonlocality often demands experiments with high complexity (defined by all parties' settings and outcomes) and multiple efficient detectors. Here, we identify the fundamental efficiency and complexity thresholds for quantum steering using two-qubit entangled states. Remarkably, it requires only one photon detector on the untrusted side, with efficiency $ε> 1/X$, where $X \geq 2$ is the number of settings on that side. This threshold applies to all pure entangled states, in contrast to analogous Bell-nonlocality tests, which require almost unentangled states to be loss-tolerant. We confirm these predictions in a minimal-complexity ($X = 2$ for the untrusted party and a single three-outcome measurement for the trusted party), detection-loophole-free photonic experiment with $ε= (51.6 \pm 0.4)\% $.

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arXiv2025

Analytical results for laser models producing a beam with sub-Poissonian photon statistics and coherence scaling as the Heisenberg limit

Recent advances in laser theory have demonstrated that a quantum enhancement is possible for the production of coherence $\mathfrak{C}$ by a continuous-wave laser device. Curiously, natural families of laser models that achieve Heisenberg-limited scaling for coherence produce the most coherence when the beam exhibits sub-Poissonian photon statistics. In this work, we provide an analytical treatment of those novel families of laser models by specializing to a parameter regime that permits a linearization. We characterize the dynamics of each laser system, and find that some of the intuitions from standard laser theory may be applied here. Specifically, the intracavity number dynamics are well-described as an Ornstein-Uhlenbeck process, while the intracavity phase dynamics are well-described in terms of a physically realizable ensemble of pure states, which evolve according to pure phase diffusion. Unlike a standard laser, however, we find that the pure states comprising the ensemble in the Heisenberg-limited lasers are substantially phase squeezed. From our dynamical analysis, we deduce various quantities of the beam for each laser family, including the first- and second-order Glauber coherence functions, intensity noise spectrum, Mandel-Q parameter and coherence $\mathfrak{C}$. In addition, inspired from these phase diffusion dynamics, we derive an upper bound on laser coherence $\mathfrak{C} \lesssim 1.1156 μ^4$ -- which is tighter by a factor of $3/8$ when compared to that derived in [Baker et al., Nat. Phys. 17 179 (2021)] -- by making one of the assumptions of that paper slightly stronger.

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arXiv2025

Properties and Applications of Partially Deterministic Polytopes

The assumption of a deterministic local hidden variable model constrains the experimentally accessible statistics in a Bell experiment to be contained in the Bell-local polytope. But what if the outputs for only a subset of the measurements at each site are predetermined by the model? In this work, we thoroughly explore this concept of `partial determinism', allowing for arbitrary numbers of parties, inputs and outputs per site. The resulting objects form new classes of convex polytopes which recover the Bell and the no-signalling polytopes as special cases. Nontrivial equivalence classes of partially deterministic models arise, which we classify completely. In particular, the Bell polytope for any scenario can be expressed in multiple different ways in terms of local partially deterministic models. This allows us to generalise Fine's theorem, recovering the original formulation as a special case, but finding new constraints otherwise. We discuss scenarios with different physical motivations, which do not require the causal structure of the Bell scenario, and where classes of partially deterministic polytopes are relevant. Our example applications include device-independent quantum state inseparability witnesses, classes of broadcast-local polytopes, and Local Friendliness scenarios in quantum foundations. We also point out instances in previous literature where classes of related objects have been studied. In the case of correlations compatible with the Local Friendliness assumptions, we find a one-to-one correspondence between partially deterministic polytopes and sequential extended Wigner's friend scenarios so that every partially deterministic polytope has physical relevance. We discuss how the framework captures a broad class of non-classicality notions, and identify an even broader notion of `composable sets', of which partially deterministic polytopes are special cases.

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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 Assemblage Tomography

A central requirement in asymmetric quantum nonlocality protocols, such as quantum steering, is the precise reconstruction of state assemblages -- statistical ensembles of quantum states correlated with remote classical signals. Here we introduce a generalized loss model for assemblage tomography that uses conical optimization techniques combined with maximum likelihood estimation. Using an evidence-based framework based on Akaike's Information Criterion, we demonstrate that our approach excels in the accuracy of reconstructions while accounting for model complexity. In comparison, standard tomographic methods fall short when applied to experimentally relevant data.

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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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arXiv2024

Experimental evidence that a photon can spend a negative amount of time in an atom cloud

When a pulse of light traverses a material, it incurs a time delay referred to as the group delay. Should the group delay experienced by photons be attributed to the time they spend as atomic excitations? However reasonable this connection may seem, it appears problematic when the frequency of the light is close to the atomic resonance, as the group delay becomes negative in this regime. To address this question, we use the cross-Kerr effect to probe the degree of atomic excitation caused by a resonant transmitted photon, by measuring the phase shift on a separate beam that is weak and off-resonant. Our results, over a range of pulse durations and optical depths, are consistent with the recent theoretical prediction that the mean atomic excitation time caused by a transmitted photon (as measured via the time integral of the observed phase shift) equals the group delay experienced by the light. Specifically, we measure mean atomic excitation times ranging from $(-0.82\pm 0.31) τ_0$ for the most narrowband pulse to $(0.54\pm 0.28) τ_0$ for the most broadband pulse, where $τ_0$ is the non-post-selected excitation time, given by the scattering (absorption) probability multiplied by the atomic lifetime $τ_{\rm sp}$. These results suggest that negative values taken by times such as the group delay have more physical significance than has generally been appreciated.

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arXiv2024

Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations

Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a non-infinitesimal time resolution. In this work, we propose a systematic assessment of the accuracy of a map. We perform error analyses for diffusive quantum trajectories, based on single-time-step Kraus operators proposed in the literature, and find the orders in time increment, $Δt$, to which such operators satisfy the conditions for valid average quantum evolution (completely positive, convex-linear, and trace-preserving), and the orders to which they match the Lindblad solutions. Given these error analyses, we propose a Kraus operator that satisfies the valid average quantum evolution conditions and agrees with the Lindblad master equation, to second order in $Δt$, thus surpassing all other existing approaches. In order to test how well our proposed operator reproduces exact quantum trajectories, we analyze two examples of qubit measurement, where exact maps can be derived: a qubit subjected to a dispersive ($z$-basis) measurement and a fluorescence (dissipative) measurement. We show analytically that our proposed operator gives the smallest average trace distance to the exact quantum trajectories, compared to existing approaches.

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arXiv2024

Experimental investigation of a multi-photon Heisenberg-limited interferometric scheme: the effect of imperfections

Interferometric phase estimation is an essential tool for precise measurements of quantities such as displacement, velocity and material properties. The lower bound on measurement uncertainty achievable with classical resources is set by the shot-noise limit (SNL) that scales asymptotically as $1/\sqrt{N}$, where $N$ is the number of resources used. The experiment of [S. Daryanoosh et al., Nat. Commun. ${\bf 9}$, 4606 (2018)] showed how to achieve the ultimate precision limit, the exact Heisenberg limit (HL), in ab-initio phase estimation with $N=3$ photon-passes, using an entangled biphoton state in combination with particular measurement techniques. The advantage of the HL over the SNL increases with the number of resources used. Here we present, and implement experimentally, a scheme for generation of the optimal $N=7$ triphoton state. We study experimentally and theoretically the generated state quality and its potential for phase estimation. We show that the expected usefulness of the prepared triphoton state for HL phase estimation is significantly degraded by even quite small experimental imperfections, such as optical mode mismatch and unwanted higher-order multi-photon terms in the states produced in parametric down-conversion.

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