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

Quantum mechanics explained

The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment

Information-disturbance tradeoff in quantum measurements

We present a simple information-disturbance tradeoff relation valid for any general measurement apparatus: The disturbance between input and output states is lower bounded by the information the apparatus provides in distinguishing these two states.Comment: 4 Pages, 1 Figure. Published version (reference added and minor changes performed

Quantum Field Theory with Null-Fronted Metrics

There is a large class of classical null-fronted metrics in which a free scalar field has an infinite number of conservation laws. In particular, if the scalar field is quantized, the number of particles is conserved. However, with more general null-fronted metrics, field quantization cannot be interpreted in terms of particle creation and annihilation operators, and the physical meaning of the theory becomes obscure.Comment: 11 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

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

Wigner's little group and Berry's phase for massless particles

The ``little group'' for massless particles (namely, the Lorentz transformations $\Lambda$ that leave a null vector invariant) is isomorphic to the Euclidean group E2: translations and rotations in a plane. We show how to obtain explicitly the rotation angle of E2 as a function of $\Lambda$ and we relate that angle to Berry's topological phase. Some particles admit both signs of helicity, and it is then possible to define a reduced density matrix for their polarization. However, that density matrix is physically meaningless, because it has no transformation law under the Lorentz group, even under ordinary rotations.Comment: 4 pages revte

Minimum error discrimination problem for pure qubit states

The necessary and sufficient conditions for minimization of the generalized rate error for discriminating among $N$ pure qubit states are reformulated in terms of Bloch vectors representing the states. For the direct optimization problem an algorithmic solution to these conditions is indicated. A solution to the inverse optimization problem is given. General results are widely illustrated by particular cases of equiprobable states and $N=2,3,4$ pure qubit states given with different prior probabilities.Comment: English is corrected thanks to PRA edito

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

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