Non-disturbing quantum measurements

We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for instance on the interplay between the number of outcomes and the Hilbert space dimension or on algebraic properties of the effect operators. We also show that (non-)disturbance is in general not a symmetric relation and that it can be decided and quantified by means of a semidefinite program.Comment: Minor corrections in v

Characterization of the Sequential Product on Quantum Effects

We present a characterization of the standard sequential product of quantum effects. The characterization is in term of algebraic, continuity and duality conditions that can be physically motivated.Comment: 11 pages. Accepted for publication in the Journal of Mathematical Physic

Strongly Incompatible Quantum Devices

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement devices, and we call this relation compatibility. Two devices are incompatible if they cannot be implemented as parts of a single measurement setup. We introduce also a more stringent notion of incompatibility, strong incompatibility. Both incompatibility and strong incompatibility are rigorously characterized and their difference is demonstrated by examples.Comment: 27 pages (AMSart), 6 figure

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

Unsharp Quantum Reality

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way

Maintaining Quantum Coherence in the Presence of Noise through State Monitoring

Unsharp POVM measurements allow the estimation and tracking of quantum wavefunctions in real-time with minimal disruption of the dynamics. Here we demonstrate that high fidelity state monitoring, and hence quantum control, is possible even in the presence of classical dephasing and amplitude noise, by simulating such measurements on a two-level system undergoing Rabi oscillations. Finite estimation fidelity is found to persist indefinitely long after the decoherence times set by the noise fields in the absence of measurement.Comment: 5 pages, 4 figure

Decoherence-assisted transport and quantum criticalities

We study the dynamics of a two-level quantum system interacting with an external environment that takes the form of an XY spin chain in the presence of an external magnetic field. While the presence of the bath itself can enhance the transition probability from the lower level to the upper level of the system, we show that this noise-assisted phenomenon is sensitive to a change of the quantum phase of the environment. The derivative of the transition probability displays a maximum in correspondence with the critical value of the applied field both in the case of isotropic and anisotropic chains

An eccentrically perturbed Tonks-Girardeau gas

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.Comment: Comments and suggestions are welcom

Solid-state memcapacitive system with negative and diverging capacitance

We suggest a possible realization of a solid-state memory capacitive (memcapacitive) system. Our approach relies on the slow polarization rate of a medium between plates of a regular capacitor. To achieve this goal, we consider a multi-layer structure embedded in a capacitor. The multi-layer structure is formed by metallic layers separated by an insulator so that non-linear electronic transport (tunneling) between the layers can occur. The suggested memcapacitor shows hysteretic charge-voltage and capacitance-voltage curves, and both negative and diverging capacitance within certain ranges of the field. This proposal can be easily realized experimentally, and indicates the possibility of information storage in memcapacitive devices

On localization and position operators in Moebius-covariant theories

Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory, thus in an intrinsic way. In particular, when Moebius covariance is present, it is possible to associate some particular transformations to the Tomita Takesaki modular operator and conjugation of a specific interval of an abstract circle. In this context we propose a way to define an operator representing the coordinate conjugated with the modular transformations. Remarkably this coordinate turns out to be compatible with the abstract notion of locality. Finally a concrete example concerning a quantum particle on a line is also given.Comment: 19 pages, UTM 705, version to appear in RM