Optimal distinction between non-orthogonal quantum states

Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability of failure. A complete solution is given to the problem of optimal distinction of three states, having arbitrary prior probabilities and arbitrary detection values. A generalization to more than three states is outlined.Comment: 9 pages LaTeX, one PostScript figure on separate pag

Convex probability domain of generalized quantum measurements

Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is shown that this point lies in a convex domain having at most d^2-1 dimensions.Comment: 7 pages LaTeX, one PostScript figure on separate pag

Terrain Database Correlation Assessment Using an Open Source Tool

Configuring networked simulators for training military teams in a distributed environment requires the usage of a set of terrain databases to represent the same training area. The results of simulation exercises can be degraded if the terrain databases are poorly correlated. A number of methodologies for determining the correlation between terrain databaHowever, there are few computational tools for this task and most of them were developed to address government needs, have limited availability, and handle specific digital formats. The goal of this paper is thus to present a novel open source tool developed as part of an academic research project.Comment: 12 pages, I/ITSEC 201

Classical interventions in quantum systems. I. The measuring process

The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. This description of the measuring process is a substantial generalization of current models in quantum measurement theory. In particular, no ancilla is needed. The final result is represented by a completely positive map of the quantum state $\rho$ (possibly with a change of the dimensions of $\rho$). A continuous limit of the above process leads to Lindblad's equation for the quantum dynamical semigroup.Comment: Final version, 14 pages LaTe

Non-linear operations in quantum information theory

Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The efficiency of the transformation of non-orthogonal states into orthogonal ones is discussed.Comment: 11 pages, LaTeX, 3 figures on separate page

Power of unentangled measurements on two antiparallel spins

We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement, whose outcomes are associated with product states. We develop analytically the upper bound 0.7935 bits to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value 0.8664 bits attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio

Experimental Demonstration of Optimal Unambiguous State Discrimination

We present the first full demonstration of unambiguous state discrimination between non-orthogonal quantum states. Using a novel free space interferometer we have realised the optimum quantum measurement scheme for two non-orthogonal states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have for the first time gained access to all three possible outcomes of this measurement. All aspects of this generalised measurement scheme, including its superiority over a standard von Neumann measurement, have been demonstrated within 1.5% of the IDP predictions

A geometric proof of the Kochen-Specker no-go theorem

We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).Comment: This paper appeared some years ago, before the author was aware of quant-ph. It is relevant to recent developments concerning Kochen-Specker theorem

Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information

When an observer wants to identify a quantum state, which is known to be one of a given set of non-orthogonal states, the act of observation causes a disturbance to that state. We investigate the tradeoff between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable non-orthogonal pure states.Comment: 20 pages, standard LaTeX, four png figures (also available from the authors: [email protected] and [email protected]

Chaotic Evolution in Quantum Mechanics

A quantum system is described, whose wave function has a complexity which increases exponentially with time. Namely, for any fixed orthonormal basis, the number of components required for an accurate representation of the wave function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure