Modal dynamics for positive operator measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how {\em deterministic} dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e. the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state $\ket{n}$. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.Comment: 14 page

What’s behind the ag-data logo? An examination of voluntary agricultural-data codes of practice

In this article, we analyse agricultural data (ag-data) codes of practice. After the introduction, Part II examines the emergence of ag-data codes of practice and provides two case studies—the American Farm Bureau’s Privacy and Security Principles for Farm Data and New Zealand’s Farm Data Code of Practice—that illustrate that the ultimate aims of ag-data codes of practice are inextricably linked to consent, disclosure, transparency and, ultimately, the building of trust. Part III highlights the commonalities and challenges of ag-data codes of practice. In Part IV several concluding observations are made. Most notably, while ag-data codes of practice may help change practices and convert complex details about ag-data contracts into something tangible, understandable and useable, it is important for agricultural industries to not hastily or uncritically accept or adopt ag-data codes of practice. There needs to be clear objectives, and a clear direction in which stakeholders want to take ag-data practices. In other words, stakeholders need to be sure about what they are trying, and able, to achieve with ag-data codes of practice. Ag-data codes of practice need credible administration, accreditation and monitoring. There also needs to be a way of reviewing and evaluating the codes in a more meaningful way than simple metrics such as the number of members: for example, we need to know something about whether the codes raise awareness and education around data practices, and, perhaps most importantly, whether they encourage changes in attitudes and behaviours around the access to and use of ag-data

Dynamical parameter estimation using realistic photodetection

We investigate the effect of imperfections in realistic detectors upon the problem of quantum state and parameter estimation by continuous monitoring of an open quantum system. Specifically, we have reexamined the system of a two-level atom with an unknown Rabi frequency introduced by Gambetta and Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct photodetection and use the realistic quantum trajectory theory reported by Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most significant effect comes from a finite bandwidth, corresponding to an uncertainty in the response time of the photodiode. Unless the bandwidth is significantly greater than the Rabi frequency, the observer's ability to obtain information about the unknown Rabi frequency, and about the state of the atom, is severely compromised. This result has implications for quantum control in the presence of unknown parameters for realistic detectors, and even for ideal detectors, as it implies that most of the information in the measurement record is contained in the precise timing of the detections.Comment: 8 pages, 6 figure

State and dynamical parameter estimation for open quantum systems

Following the evolution of an open quantum system requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega$, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the $x$ quadrature, homodyne of the $y$ quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure

Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections

The extension of quantum trajectory theory to incorporate realistic imperfections in the measurement of solid-state qubits is important for quantum computation, particularly for the purposes of state preparation and error-correction as well as for readout of computations. Previously this has been achieved for low-frequency (dc) weak measurements. In this paper we extend realistic quantum trajectory theory to include radio frequency (rf) weak measurements where a low-transparency quantum point contact (QPC), coupled to a charge qubit, is used to damp a classical oscillator circuit. The resulting realistic quantum trajectory equation must be solved numerically. We present an analytical result for the limit of large dissipation within the oscillator (relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode of operation is considered. Here the QPC is biased (dc) as well as subjected to a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be a low-efficiency charge-qubit detector, that may nevertheless be higher than the dc-QPC (which is subject to 1/f noise).Comment: 12 pages, 2 colour figures. v3 is published version (minor changes since v2

The interpretation of non-Markovian stochastic Schr\"odinger equations as a hidden-variable theory

Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A 66, 012108 (2002)] we investigated this question using the orthodox interpretation of quantum mechanics. We found that the solution of a non-Markovian SSE represents the state the system would be in at that time if a measurement was performed on the environment at that time, and yielded a particular result. However, the linking of solutions at different times to make a trajectory is, we concluded, a fiction. In this paper we investigate this question using the modal (hidden variable) interpretation of quantum mechanics. We find that the noise function $z(t)$ appearing in the non-Markovian SSE can be interpreted as a hidden variable for the environment. That is, some chosen property (beable) of the environment has a definite value $z(t)$ even in the absence of measurement on the environment. The non-Markovian SSE gives the evolution of the state of the system ``conditioned'' on this environment hidden variable. We present the theory for diffusive non-Markovian SSEs that have as their Markovian limit SSEs corresponding to homodyne and heterodyne detection, as well as one which has no Markovian limit.Comment: 9 page

Fluorescence Intensity and Intermittency as Tools for Following Dopamine Bioconjugate Processing in Living Cells

CdSe/ZnS quantum dots (QDs) conjugated to biomolecules that quench their fluorescence, particularly dopamine, have particular spectral properties that allow determination of the number of conjugates per particle, namely, photoenhancement and photobleaching. In this work, we quantify these properties on a single-particle and ensemble basis in order to evaluate their usefulness as a tool for indicating QD uptake, breakdown, and processing in living cells. This creates a general framework for the use of fluorescence quenching and intermittency to better understand nanoparticle-cell interactions