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John Gough

Publications and source records attributed to John Gough.

At least 19 recordsLinked to original sources
arXiv2026

Discretisation of quantum feedback networks for implementation on a quantum computer

Quantum Feedback Network Theory (also known colloquially as the SLH-framework) is a powerful tool for modeling systems in quantum optics. This paper describes a method for discretising SLH-networks such that they can be implemented on a quantum computer. Building on a discretisation theorem for quantum stochastic differential equations, we establish strong convergence, uniformly on compact time intervals, of the discretised system to the continuous SLH-network as the discretisation mesh goes to zero.

quant-ph↗
arXiv2026

Quantum Filtering for Squeezed Noise Inputs

We derive the quantum filter for a quantum open system undergoing quadrature measurements (homodyning) where the input field is in a general quasi-free state. This extends previous work for thermal input noise and allows for squeezed inputs. We introduce a convenient class of Bogoliubov transformations which we refer to as balanced and formulate the quantum stochastic model with squeezed noise as an Araki-Woods type representation. We make an essential use of the Tomita-Takesaki theory to construct the commutant of the C*-algebra describing the inputs and obtain the filtering equations using the quantum reference probability technique. The derived quantum filter must be independent of the choice of representation and this is achieved by fixing an independent quadrature in the commutant algebra.

quant-ph↗
arXiv2026

The Universe as a Detector: A Quantum Filtering Formulation of the Diósi-Penrose Model

We consider the Diósi-Penrose problem but rather than postulating background gravitational fluctuations, we instead consider the quantum filter that arises from space-time homodyning the continuum of output quadrature described in the open quantum stochastic model presented here. This is described by a quantum Kushner-Stratonovich equation, typical of the form appearing in continuous-time collapse of the wave-function models in Quantum Decoherence Theory

quant-ph↗
arXiv2026

Quantum Filtering at Finite Temperature

We pose and solve the problem of quantum filtering based on continuous-in-time quadrature measurements (homodyning) for the case where the quantum process is in a thermal state. The standard construction of quantum filters involves the determination of the conditional expectation onto the von Neumann algebra generated by the measured observables with the non-demolition principle telling us to restrict the domain (the observables to be estimated) to the commutant of the algebra. The finite-temperature case, however, has additional structure: we use the Araki-Woods representation for the measured quadratures, but the Tomita-Takesaki theory tells us that there exists a separate, commuting representation and therefore the commutant will have a richer structure than encountered in the Fock vacuum case. We apply this to the question of quantum trajectories to the Davies-Fulling-Unruh model. Here, the two representations are interpreted as the fields in the right and left Rindler wedges.

quant-ph↗
arXiv2025

Quantum White Noises and The Master Equation for Gaussian Reference States

We show that a basic quantum white noise process formally reproduces quantum stochastic calculus when the appropriate normal / chronological orderings are prescribed. By normal ordering techniques for integral equations and a generalization of the Araki-Woods representation, we derive the master and random Heisenberg equations for an arbitrary Gaussian state: this includes thermal and squeezed states.

quant-ph↗
arXiv2017

The Tyranny of Qubits - Quantum Technology's Scalability Bottleneck

In this essay, I look at (bemoan) the issues surrounding simulating quantum systems in order to design quantum devices for quantum technologies. The program runs into a natural difficulty that simulating quantum systems really require a proper quantum simulator. The problem is likened to the "tyranny of numbers" that faced computer engineers in the 1960s.

quant-ph↗
arXiv2016

The Kalman Decomposition for Linear Quantum Stochastic Systems

The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like factorization of [2] on the observability matrix of the system.

quant-ph↗
arXiv2016

Noether theorems and quantum anomalies

In this communication, we show that both infinite-dimensional versions of Noether's theorems, and the explanation of quantum anomalies can be obtained using similar formulas for the derivatives of functions whose values are measures (Smolyanov and von Weizsaecker, 1995) or pseudomeasures (Gough, Ratiu and Smolyanov, 2015). In particular, we improve son these results.

math-ph↗
arXiv2016

Non-Markovian Quantum Feedback Networks I: Quantum Transmission Lines, Lossless Bounded Real Property and Limit Markovian Channels

The purpose of this paper is to set out the problems of modeling quantum communication and signal processing where the communication between systems via a non-Markovian channel. This is a general feature of quantum transmission lines. Our ultimate objective is to extend the networks rules that have been developed for Markovian models. To this end we recall the Hamiltonian description of such non-Markov models of transmission lines and their quantization. These have occurred in the context of non-quilibrium thermodynamics, but our interest is in the transmission lines as carriers of information rather than heat baths. We show that there is an analytic scattering matrix associated with these models and that stability may be formulated in terms of the lossless bounded real property. Noting that the input and output fields do not separately satisfy a non-self- demolition principle, we discuss the rigorous limit in which such models appear Markov and so amenable to standard approaches of quantum filtering and control

quant-ph↗
arXiv2016

Quantum Trajectories for Squeezed Input Processes: Explicit Solutions

We consider the quantum (trajectories) filtering equation for the case when the system is driven by Bose field inputs prepared in an arbitrary non-zero mean Gaussian state. The a posteriori evolution of the system is conditioned by the results of a single or double homodyne measurements. The system interacting with the Bose field is a single cavity mode taken initially in a Gaussian state. We show explicit solutions using the method of characteristic functions to the filtering equations exploiting the linear Gaussian nature of the problem.

quant-ph↗
arXiv2016

Interferometric Phase Estimation Though Quantum Filtering in Coherent States

We derive the form of the quantum filter equation describing the continuous observation of the phase of a quantum system in an arm of an interferometer via non-demolition measurements when the statistics of an input field used for the indirect measurement are in a general coherent state. Both quadrature homodyne detection and photon-counting dection schemes are covered, and we solve the linearized filter for a specific application.

quant-ph↗
arXiv2015

Symplectic Noise & The Classical Analog of the Lindblad Generator

We introduce the concepts of Poisson brackets for classical noise, and of canonically conjugate Wiener processes (symplectic noise). Phase space diffusions driven by these processes are considered and the general form of a stochastic process preserving the full (system and noise) Poisson structure is obtained. We show that, once the classical stochastic model is required to preserve the joint system and noise Poisson bracket, it has much in common with quantum markovian models.

quant-ph↗
arXiv2015

A Trotter-Kato Theorem for Quantum Markov Limits

Using the Trotter-Kato theorem we prove the convergence of the unitary dynamics generated by an increasingly singular Hamiltonian in the case of a single field coupling. The limit dynamics is a quantum stochastic evolution of Hudson-Parthasarathy type, and we establish in the process a graph limit convergence of the pre-limit Hamiltonian operators to the Chebotarev-Gregoratti-von Waldenfels Hamiltonian generating the quantum Ito evolution.

math-ph↗
arXiv2014

Belavkin Filtering with Squeezed Light Sources

We derive the filtering equation for Markovian systems undergoing homodyne measurement in the situation where the output processes being monitored are squeezed. The filtering theory applies to case where the system is driven by Fock noise (that, quantum input processes in a coherent state) and where the output is mixed with a squeezed signal. It also applies to the case of a system driven by squeezed noise, but here there is a physical restriction to emission/absorption coupling only. For the special case of a cavity mode where the dynamics is linear, we are able to derive explicitly the filtered estimate $π_t (a)$ for the mode annihilator $a$ based on the homodyne quadrature observations up to time $t$.

quant-ph↗
arXiv2014

Coherent feedback control in quantum transport

We discuss control of the quantum-transport properties of a mesoscopic device by connecting it in a coherent feedback loop with a quantum-mechanical controller. We work in a scattering approach and derive results for the combined scattering matrix of the device-controller system and determine the conditions under which the controller can exert ideal control on the output characteristics. As concrete example we consider the use of feedback to optimise the conductance of a chaotic quantum dot and investigate effects of controller dimension and decoherence. In both respects we find that the performance of the feedback geometry is well in excess of that offered by a simple series configuration.

cond-mat.mes-hall↗
arXiv2014

Heisenberg Picture Approach to the Stability of Quantum Markov Systems

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

math-ph↗
arXiv2013

Quantum Filtering in Coherent States

We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state.

math-ph↗