Related papers: Reconstructing the density operator via simple pro…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if $p$ is a positive contraction in an operator system $V$ which satisfies certain…
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
Measurement is the only part of a general quantum system that has yet to be characterized experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully…
We derive on the basis of Bayes' theorem a simple but general expression for the retrodicted premeasurement state associated with the result of any measurement. The retrodictive density operator is the normalised probability operator…
Measurement of a quantum system provides information concerning the state in which it was prepared. In this paper we show how the retrodictive formalism can be used to evaluate the probability associated with any one of a given set of…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
A minimal set of measurement operators for quantum state tomography has in the non-degenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here, we consider the situation where the…
No quantum system can be considered totally isolated from its environment. In most cases the interaction between the system of interest and the external degrees of freedom deeply changes its dynamics, as described by open quantum system…
We present a general method for constructing pure-product-state representations for density operators of $N$ quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
A density operator, $\rho = {P}_{\alpha } |\alpha > <\alpha | + {P}_{\beta } |\beta > <\beta |$, with ${P}_{\alpha }$ and ${P}_{\beta }$ linearly independent normalized wave functions, must be traced normalized, so ${P}_{\beta } = 1 -…
We discuss a scheme for reconstructing experimentally the diagonal elements of the density matrix of quantum optical states. Applications to PDC heralded photons, multi-thermal and attenuated coherent states are illustrated and discussed in…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…