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Open quantum systems are harder to track than open classical systemsMay 27 2019For a Markovian open quantum system it is possible, by continuously monitoring the environment, to know the stochastically evolving pure state of the system without altering the master equation. In general, even for a system with a finite Hilbert space ... More

Rapid readout of a register of qubits using open loop quantum controlOct 30 2014Measurements are a primitive for characterizing quantum systems. Reducing the time taken to perform a measurement may be beneficial in many areas of quantum information processing. We show that permuting the eigenvalues of the state matrix in the logical ... More

Does nonlinear metrology offer improved resolution? Answers from quantum information theoryMay 11 2012Nov 02 2012A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the mean photon ... More

Heisenberg-style bounds for arbitrary estimates of shift parameters including prior informationJan 22 2012Mar 29 2012A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2|G|> where G is the generator of the shift (with an arbitrary ... More

Entanglement verification and steering when Alice and Bob cannot be trustedOct 22 2012Mar 14 2013Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of trust required, between the referee and each observer. ... More

Nonlocality in Bell's theorem, in Bohm's theory, and in Many Interacting Worlds theorisingJul 04 2018Sep 04 2018'Locality' is a fraught word, even within the restricted context of Bell's theorem. As one of us has argued elsewhere, that is partly because Bell himself used the word with different meanings at different stages in his career. The original, weaker, meaning ... More

Stochastic Heisenberg limit: Optimal estimation of a fluctuating phaseJun 06 2013Sep 04 2013The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p ... More

Quantum phenomena modelled by interactions between many classical worldsFeb 25 2014Oct 26 2014We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between these worlds, ... More

Experimental test of universal complementarity relationsNov 02 2012May 30 2013Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental verification of universally ... More

Reference frame independent Einstein-Podolsky-Rosen steeringNov 22 2016Protocols for testing or exploiting quantum correlations-such as entanglement, Bell nonlocality, and Einstein-Podolsky-Rosen steering- generally assume a common reference frame between two parties. Establishing such a frame is resource-intensive, and ... More

Experimental quantum processing enhancement in modelling stochastic processesFeb 18 2016Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their future behaviour ... More

Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimatesSep 17 2012Nov 19 2012The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The ... More

Implementation of a canonical phase measurement with quantum feedbackJun 17 2019Much of modern metrology and communication technology encodes information in electromagnetic waves, typically as an amplitude or phase. While current hardware can perform near-ideal measurements of photon number or field amplitude, to date no device exists ... More

Necessary Condition for Steerability of Arbitrary Two-Qubit States with LossOct 31 2017Einstein-Podolsky-Rosen steering refers to the quantum phenomenon whereby the state of a system held by one party can be "steered" into different states at the will of another, distant, party by performing different local measurements. Although steering ... More

Ground states in the Many Interacting Worlds approachDec 05 2017Jan 03 2018Recently the Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions was proposed. This approach leads quite naturally to numerical integrators of the Schr\"odinger equation. It has been suggested that such integrators may feature ... More

On the dynamics of initially correlated open quantum systems: theory and applicationsOct 30 2018We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of $d^2$ (or less) completely positive maps, where $d$ is the dimension of the system. Only one such map is required for the ... More

Volume monogamy of quantum steering ellipsoids for multi-qubit systemsJun 08 2016Oct 07 2016The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit ... More

Observing momentum disturbance in double-slit "which-way" measurementsMay 05 2018Making a "which-way" measurement (WWM) to identify which slit a particle goes through in a double-slit apparatus will reduce the visibility of interference fringes. There has been a long-standing controversy over whether this can be attributed to an uncontrollable ... More

How many principles does it take to change a light bulb ... into a laser?Oct 16 2015Feb 03 2016Quantum optics did not, and could not, flourish without the laser. The present paper is not about the principles of laser construction, still less a history of how the laser was invented. Rather, it addresses the question: what are the fundamental features ... More

What is an atom laser?Nov 20 1996An atom laser is a hypothetical device which would produce an atomic field analogous to the electromagnetic field of a photon laser. Here I argue that for this analogy to be meaningful it is necessary to have a precise definition of a laser which applies ... More

Reply to Elsässer's Comment on "How many principles does it take to change a light bulb ... into a laser?"Jul 31 2016In his Comment, Els\"asser claims that the answer to my titular question is one, not four as I have it. He goes on to give the singular principle that supposedly captures the difference between a light-bulb and a laser: $g^{(2)}(\tau=0)=1$. His claim ... More

Quantum discord is Bohr's notion of non-mechanical disturbance introduced in his answer to EPRAug 24 2012May 03 2013By rigorously formalizing the Einstein-Podolsky-Rosen (EPR) argument, and Bohr's reply, one can appreciate that both arguments were technically correct. Their opposed conclusions about the completeness of quantum mechanics hinged upon an explicit difference ... More

Defending Continuous Variable Teleportation: Why a laser is a clock, not a quantum channelMar 19 2004It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87}, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Van Enk, ... More

Quantum State EffusionSep 21 2016I give a scientific perspective, with a personal emphasis, on the seminal 1992 paper, "The quantum-state diffusion model applied to open systems", by Gisin and Percival.

The Two Bell's Theorems of John BellFeb 03 2014Jun 19 2014Many of the heated arguments about the meaning of "Bell's theorem" arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena ... More

Comment on ``Testing integrability with a single bit of quantum information''May 25 2003In quant-ph/0303042, Poulin, Laflamme, Milburn and Paz consider the problem of distinguishing quantum chaos from quantum integrability for dynamics in an $N$-dimensional Hilbert space. They claim that this can be done by deterministic quantum computing ... More

Optical coherence and teleportation: Why a laser is a clock, not a quantum channelMar 19 2003It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87}, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Van Enk, ... More

Conclusive experimental demonstration of one-way Einstein-Podolsky-Rosen steeringJun 27 2018Sep 12 2018Einstein-Podolsky-Rosen steering is a quantum phenomenon wherein one party influences, or steers, the state of a distant party's particle beyond what could be achieved with a separable state, by making measurements on one half of an entangled state. This ... More

Conclusive quantum steering with superconducting transition edge sensorsNov 03 2011Jan 11 2012Quantum steering allows two parties to verify shared entanglement even if one measurement device is untrusted. A conclusive demonstration of steering through the violation of a steering inequality is of considerable fundamental interest and opens up applications ... More

Maximum information gain in weak or continuous measurements of qudits: complementarity is not enoughMay 04 2011Jan 15 2012To maximize average information gain for a classical measurement, all outcomes of an observation must be equally likely. The condition of equally likely outcomes may be enforced in quantum theory by ensuring that one's state $\rho$ is maximally different, ... More

Comments on toric varietiesOct 21 2003Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint arXiv:math.AG/0306221. That is, they focus on the fact that toric varieties are ... More

Toric singularities revisitedMay 30 2003Mar 04 2005In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to ... More

Quantum feedback for rapid state preparation in the presence of control imperfectionsFeb 28 2011Aug 09 2011Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an $x$ eigenstate from a mixed ... More

Quantum Jumps Are More Quantum Than Quantum DiffusionDec 06 2013It was recently argued [Phys. Rev. Lett 108, 220402 (2012)] that the stochastic dynamics of an open quantum system are not inherent to the system, but rather depend on the existence and nature of a distant detector. The proposed experimental tests involved ... More

Why does Boltzmann's ergodic hypothesis work and when does it failOct 19 2005According to a recently given ergodic condition for Hermitian many-body models the thermodynamic limit and irreversibility are necessary but by themselves not sufficient. The sufficient condition turns out to be the existence of a zero frequency mode. ... More

Optimality of feedback control strategies for qubit purificationJul 20 2007Jul 25 2007Recently two papers [K. Jacobs, Phys. Rev. A {\bf 67}, 030301(R) (2003); H. M. Wiseman and J. F. Ralph, New J. Physics {\bf 8}, 90 (2006)] have derived control strategies for rapid purification of qubits, optimized with respect to various goals. In the ... More

Precision bounds for noisy nonlinear quantum metrologySep 09 2013Feb 14 2014We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon ... More

Fan is to monoid as scheme is to ring: a generalization of the notion of a fanJun 13 2003Jul 08 2004Following DeMeyer, Ford & Miranda [DFM93], we define a topology on a fan by declaring open sets to be its subfans. Then, like Kato [Kat94], we make our fans into monoided spaces by associating a sheaf of monoids to each fan. (Our sheaf of monoids differs ... More

The zig-zag road to realityJul 25 2011In the standard model of particle physics, all fermions are fundamentally massless and only acquire their effective bare mass when the Higgs field condenses. Therefore, in a fundamental de Broglie-Bohm pilot-wave quantum field theory (valid before and ... More

Optimal control of entanglement via quantum feedbackOct 01 2006It has recently been shown that finding the optimal measurement on the environment for stationary Linear Quadratic Gaussian control problems is a semi-definite program. We apply this technique to the control of the EPR-correlations between two bosonic ... More

Loophole-free Einstein-Podolsky-Rosen experiment via quantum steeringNov 03 2011Apr 04 2012Tests of the predictions of quantum mechanics for entangled systems have provided increasing evidence against local realistic theories. However, there still remains the crucial challenge of simultaneously closing all major loopholes - the locality, freedom-of-choice, ... More

Single Spin Measurement using Single Electron Transistors to Probe Two Electron SystemsMar 25 1999Jun 17 1999We present a method for measuring single spins embedded in a solid by probing two electron systems with a single electron transistor (SET). Restrictions imposed by the Pauli Principle on allowed two electron states mean that the spin state of such systems ... More

Heterodyne and adaptive phase measurements on states of fixed mean photon numberDec 11 1998Sep 19 2002The standard technique for measuring the phase of a single mode field is heterodyne detection. Such a measurement may have an uncertainty far above the intrinsic quantum phase uncertainty of the state. Recently it has been shown [H. M. Wiseman and R. ... More

Quantum noise in the position measurement of a cavity mirror undergoing Brownian motionFeb 10 1999We perform a quantum theoretical calculation of the noise power spectrum for a phase measurement of the light output from a coherently driven optical cavity with a freely moving rear mirror. We examine how the noise resulting from the quantum back action ... More

Are dynamical quantum jumps detector-dependent?Oct 01 2011Apr 19 2012Dynamical quantum jumps were initially conceived by Bohr as objective events associated with the emission of a light quantum by an atom. Since the early 1990s they have come to be understood as being associated rather with the detection of a photon by ... More

Centre-finding in E. coli and the role of mathematical modelling: past, present and futureJan 18 2019We review the key role played by mathematical modelling in elucidating two centre-finding patterning systems in E. coli: midcell division positioning by the MinCDE system and DNA partitioning by the ParABS system. We focus particularly on how, despite ... More

Pure-state quantum trajectories for general non-Markovian systems do not existJun 18 2008Sep 30 2008Since the first derivation of non-Markovian stochastic Schr\"odinger equations, their interpretation has been contentious. In a recent Letter [Phys. Rev. Lett. 100, 080401 (2008)], Di\'osi claimed to prove that they generate "true single system trajectories ... More

Spin effects in the inspiral of coalescing compact binariesNov 19 1992We derive the contributions of spin-orbit and spin-spin coupling to the gravitational radiation from coalescing binary systems of spinning compact objects. We calculate spin effects in the symmetric, trace-free radiative multipoles that determine the ... More

Discord in relation to resource states for measurement-based quantum computationJul 03 2013Mar 14 2014We consider the issue of what should count as a resource for measurement-based quantum computation (MBQC). While a state that supports universal quantum computation clearly should be considered a resource, universality should not be necessary given the ... More

Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)Nov 12 2009Jun 13 2012The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of \emph{signal locality} plus \emph{predictability} ... More

Reply to Norsen's paper "Are there really two different Bell's theorems?"Mar 24 2015Yes. That is my polemical reply to the titular question in Travis Norsen's self-styled "polemical response to Howard Wiseman's recent paper." Less polemically, I am pleased to see that on two of my positions --- that Bell's 1964 theorem is different from ... More

Tracking an open quantum system using a finite state machine: stability analysisJun 21 2011A finite-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create a trajectory ... More

Efficient tracking of the state of a qubitApr 23 2011We study resource requirements for tracking the state of an open qubit subject to continuous observation. This problem is of great importance for quantum control.

Coherent feedback that beats all measurement-based feedback protocolsNov 07 2012Jul 21 2014We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in ... More

Global versus local optimality in feedback-controlled qubit purification: new insights from minimizing Rényi entropiesDec 04 2013Aug 07 2014It was first shown by Jacobs, in 2003, that the process of qubit state purification by continuous measurement of one observable can be enhanced, on average, by unitary feedback control. Here, we quantify this by the reduction in any one of the family ... More

Adaptive phase measurements for narrowband squeezed beamsMar 22 2006We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and hence can be significantly ... More

Quantum state smoothing: Why the types of observed and unobserved measurements matterApr 08 2019We investigate the estimation technique called quantum state smoothing introduced by Guevara and Wiseman [Phys.~Rev.~Lett.~{\bf 115}, 180407 (2015)], which offers a valid quantum state estimate for a partially monitored system, conditioned on the observed ... More

Causarum Investigatio and the Two Bell's Theorems of John BellMar 22 2015"Bell's theorem" can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem ... More

Rapid Measurement of Quantum Systems using Feedback ControlDec 21 2007Apr 29 2008We introduce a feedback control algorithm that increases the speed at which a measurement extracts information about a $d$-dimensional system by a factor that scales as $d^2$. Generalizing this algorithm, we apply it to a register of $n$ qubits and show ... More

Stochastic feedback control of quantum transport to realize a dynamical ensemble of two nonorthogonal pure statesOct 17 2015A Markovian open quantum system which relaxes to a unique steady state $\rho_{ss}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by Karasik and Wiseman [Phys. Rev. Lett. 106, 020406 ... More

Necessary conditions for steerability of two qubits, from consideration of local operationsJun 11 2019EPR-steering refers to the ability of one observer to convince a distant observer that they share entanglement by making local measurements. Determining which states allow a demonstration of EPR-steering remains an open problem in general, even for the ... More

A partition of connected graphsMay 09 2005We define an algorithm k which takes a connected graph G on a totally ordered vertex set and returns an increasing tree R (which is not necessarily a subtree of G). We characterize the set of graphs G such that k(G)=R. Because this set has a simple structure ... More

The generalized recurrent set and strong chain recurrenceDec 10 2015Mar 05 2016Fathi and Pageault have recently shown a connection between Auslander's generalized recurrent set $GR(f)$ and Easton's strong chain recurrent set. We study $GR(f)$ by examining that connection in more detail, as well as connections with other notions ... More

Irrelevant Exceptional Divisors for Curves on a Smooth SurfaceNov 24 2006Aug 28 2007Given a singular curve on a smooth surface, we determine which exceptional divisors on the minimal resolution of that curve contribute toward its jumping numbers.

A molecular dynamics test of the Navier-Stokes-Fourier paradigm for compressible gaseous continuaJan 08 2013Jan 24 2013Knudsen's pioneering experimental and theoretical work performed more than a century ago pointed to the fact that the Navier-Stokes-Fourier (NSF) paradigm is inapplicable to compressible gases at Knudsen numbers (Kn) beyond the continuum range, namely ... More

A Live Maxwell's DemonMay 22 2019Jun 03 2019The first direct experimental replication of the Maxwell Demon thought experiment is outlined. The experiment determines the velocity/kinetic energy distribution of the particles in a sample by a novel interpretation of the results from a standard time-of-flight ... More

Non-local model for surface tension in fluid-fluid simulationsJun 24 2019We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support $3.5\varepsilon$ added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically ... More

Fundamental Quantum Limit to Waveform EstimationJun 28 2010Mar 04 2011We derive a quantum Cram\'er-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and atomic magnetometers. ... More

Exploring Lattice Quantum Chromodynamics by CoolingSep 13 1994The effect of cooling on a number of observables is calculated in SU(2) lattice gauge theory. The static quark-antiquark potential and spin-dependent interactions are studied, and the topological charge is monitored. The chiral symmetry breaking order ... More

Geodesics and Spanning Trees for Euclidean First-Passage PercolationOct 21 2000The metric $D_\alpha (q,q')$ on the set $Q$ of particle locations of a homogeneous Poisson process on $R^d$, defined as the infimum of $(\sum_i |q_i - q_{i+1}|^\alpha)^{1/\alpha}$ over sequences in $Q$ starting with $q$ and ending with $q'$ (where $| ... More

Fourier and Gegenbauer Expansions for a Fundamental Solution of Laplace's Equation in Hyperspherical GeometryMay 19 2014Feb 14 2015For a fundamental solution of Laplace's equation on the $R$-radius $d$-dimensional hypersphere, we compute the azimuthal Fourier coefficients in closed form in two and three dimensions. We also compute the Gegenbauer polynomial expansion for a fundamental ... More

Reply to Gillis's "On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel"Aug 14 2016We address Gillis' recent criticism [arXiv:1506.05795] of a series of papers (by different combinations of the present authors) on formulations of Bell's theorem. Those papers intended to address an unfortunate gap of communication between two broad camps ... More

Detector dependency of diffusive quantum monitoringsMay 01 2015Continuous measurements play a pivotal role in the study of dynamical open quantum systems. `Dyne' detections are among the most widespread and efficient measurement schemes, and give rise to quantum diffusion of the conditioned state. In this work we ... More

Ferreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rulesSep 04 2003Entanglement is a resource central to quantum information (QI). In particular, entanglement shared between two distant parties allows them to do certain tasks that would otherwise be impossible. In this context, we study the effect on the available entanglement ... More

Loss-Tolerant Tests Of Einstein-Podolsky-Rosen-SteeringOct 30 2013We analyse two classes of Einstein-Podolsky-Rosen (EPR)-steering inequalities, the violation of which can be used to demonstrate EPR-steering with an entangled two-qubit Werner state: linear inequalities and quadratic inequalities. We discuss how post-selection ... More

The present-day mass-metallicity relation for galaxies using a new electron-temperature methodJan 09 2019We present a study of electron temperatures (Te) and gas-phase oxygen abundances (Z_Te) for galaxies in the local Universe (z<0.25). Our sample comprises spectra from a total of 264 emission-line systems, ranging from individual HII regions to whole galaxies, ... More

Quantum State SmoothingMar 10 2015Nov 03 2015Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both past and future) observations. Here we define a smoothed quantum state for a partially monitored ... More

Qubit purification speed-up for three complementary continuous measurementsJan 18 2012We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators \sigma_x, \sigma_y, \sigma_z. The purification dynamics is quantified by (i) the average purification rate, and (ii) the mean time of reaching ... More

Replacing Quantum Feedback with Open-Loop Control and Quantum FilteringAug 03 2009Mar 24 2010Feedback control protocols can stabilize and enhance the operation of quantum devices, however, unavoidable delays in the feedback loop adversely affect their performance. We introduce a quantum control methodology, combining open-loop control with quantum ... More

Concepts of quantum non-Markovianity: a hierarchyDec 24 2017Jul 06 2018Markovian approximation is a widely-employed idea in descriptions of the dynamics of open quantum systems (OQSs). Although it is usually claimed to be a concept inspired by classical Markovianity, the term quantum Markovianity is used inconsistently and ... More

An Entangled Web of Crime: Bell's Theorem as a Short StoryApr 26 2005Non-locality of the type first elucidated by Bell in 1964 is a difficult concept to explain to non-specialists and undergraduates. Here we attempt this by showing how such non-locality can be used to solve a problem in which someone might find themselves ... More

Entanglement of indistinguishable particles in condensed matter physicsJan 12 2006Oct 13 2006The concept of entanglement in systems where the particles are indistinguishable has been the subject of much recent interest and controversy. In this paper we study the notion of entanglement of particles introduced by Wiseman and Vaccaro [Phys. Rev. ... More

Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and ComplementarityOct 06 2010Sep 01 2011In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations which he dramatized using a parable about a seer who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it ... More

Quantum filtering of a thermal master equation with purified reservoirNov 05 2014Dec 16 2014We consider a system subject to a quantum optical master equation at finite temperature and study a class of conditional dynamics obtained by monitoring its totally or partially purified environment. More specifically, drawing from the notion that the ... More

Adaptive estimation of a time-varying phase with power-law spectrumDec 02 2016When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\omega|^p$ with $p>1$, then the generalized ... More

Deterministic preparation of superpositions of vacuum plus one photon by adaptive homodyne detection: experimental considerationsMar 20 2014Jul 25 2014The preparation stage of optical qubits is an essential task in all the experimental setups employed for the test and demonstration of Quantum Optics principles. We consider a deterministic protocol for the preparation of qubits as a superposition of ... More

Entanglement of identical particles and reference phase uncertaintyNov 06 2003Feb 17 2004We have recently introduced a measure of the bipartite entanglement of identical particles, E_P, based on the principle that entanglement should be accessible for use as a resource in quantum information processing. We show here that particle entanglement ... More

Quantum State Smoothing for Linear Gaussian SystemsJan 02 2019Quantum 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 ... More

An interleaved sampling scheme for the characterization of single qubit dynamicsMar 22 2010Dec 07 2011In this paper, we demonstrate that interleaved sampling techniques can be used to characterize the Hamiltonian of a qubit and its environmental decoherence rate. The technique offers a significant advantage in terms of the number of measurements that ... More

Quantum trajectories for the realistic measurement of a solid-state charge qubitJan 13 2004Dec 23 2004We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector ... More

Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approachJun 22 2000Jan 15 2001We obtain the finite-temperature unconditional master equation of the density matrix for two coupled quantum dots (CQD) when one dot is subjected to a measurement of its electron occupation number using a point contact (PC). To determine how the CQD system ... More

Evidence that highly non-uniform black strings have a conical waistApr 08 2003Jun 29 2003Numerical methods have allowed the construction of vacuum non-uniform strings. For sufficient non-uniformity, the local geometry about the minimal horizon sphere (the "waist") was conjectured to be a cone metric. We are able to test this conjecture explicitly ... More

Amortized Bethe Free Energy Minimization for Learning MRFsJun 14 2019We propose to learn deep undirected graphical models (i.e., MRFs), with a non-ELBO objective for which we can calculate exact gradients. In particular, we optimize a saddle-point objective deriving from the Bethe free energy approximation to the partition ... More

A fixed point theorem for bounded dynamical systemsAug 08 2001Sep 23 2002We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$ intersects W then ... More

Analytical steady-state solutions for pressure with a multiscale non-local model for two-fluid systemsMay 16 2019May 21 2019We consider the nonlocal multiscale model for surface tension \citep{Tartakovsky2018} as an alternative to the (macroscale) Young-Laplace law. The nonlocal model is obtained in the form of an integral of a molecular-force-like function with support $\varepsilon$ ... More

Some dual definite integrals for Bessel functionsSep 24 2015Based on known definite integrals of Bessel functions of the first kind, we obtain exact solutions to unknown definite integrals using the method of integral transforms from Hankel's transform.

Bounded homeomorphisms of the open annulusSep 23 2002We prove a generalization of the Poincar\'e-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the study of bounded ... More

A geometric view of quantum cellular automataAug 15 2012Nielsen, et al. [1, 2] proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of the space of ... More

Influence-free states on compound quantum systemsJul 12 2005Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of quantum-mechanical mixed ... More

Fundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant CurvatureMar 19 2018Dec 31 2018We perform global and local analysis of oscillatory and damped spherically symmetric fundamental solutions for Helmholtz operators $\big({-}\Delta\pm\beta^2\big)$ in $d$-dimensional, $R$-radius hyperbolic ${\mathbf H}_R^d$ and hyperspherical ${\mathbf ... More