Bluff your way in the second law of thermodynamics

The aim of this article is to analyze the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-(a)symmetry and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Carath\'eodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-asymmetry plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. Key words: thermodynamics, second law, irreversibility, time-asymmetry, arrow of time.Comment: Studies in History and Philosophy of Modern Physics (to appear

Strengthened Bell inequalities for orthogonal spin directions

We strengthen the bound on the correlations of two spin-1/2 particles (qubits) in separable (non-entangled) states for locally orthogonal spin directions by much tighter bounds than the well-known Bell inequality. This provides a sharper criterion for the experimental distinction between entangled and separable states, and even one which is a necessary and sufficient condition for separability. However, these improved bounds do not apply to local hidden-variable theories, and hence they provide a criterion to test the correlations allowed by local hidden-variable theories against those allowed by separable quantum states. Furthermore, these bounds are stronger than some recent alternative experimentally accessible entanglement criteria. We also address the issue of finding a finite subset of these inequalities that would already form a necessary and sufficient condition for non-entanglement. For mixed state we have not been able to resolve this, but for pure states a set of six inequalities using only three sets of orthogonal observables is shown to be already necessary and sufficient for separability.Comment: v2: Considerably changed, many new and stronger results v3: Published version; To appear in Physics Letters A. Online available from publishers websit

Inequalities that test locality in quantum mechanics

Quantum theory violates Bell's inequality, but not to the maximum extent that is logically possible. We derive inequalities (generalizations of Cirel'son's inequality) that quantify the upper bound of the violation, both for the standard formalism and the formalism of generalized observables (POVMs). These inequalities are quantum analogues of Bell inequalities, and they can be used to test the quantum version of locality. We discuss the nature of this kind of locality. We also go into the relation of our results to an argument by Popescu and Rohrlich (Found. Phys. 24, 379 (1994)) that there is no general connection between the existence of Cirel'son's bound and locality.Comment: 5 pages, 1 figure; the argument has been made clearer in the revised version; 1 reference adde

Partial separability and entanglement criteria for multiqubit quantum states

We explore the subtle relationships between partial separability and entanglement of subsystems in multiqubit quantum states and give experimentally accessible conditions that distinguish between various classes and levels of partial separability in a hierarchical order. These conditions take the form of bounds on the correlations of locally orthogonal observables. Violations of such inequalities give strong sufficient criteria for various forms of partial inseparability and multiqubit entanglement. The strength of these criteria is illustrated by showing that they are stronger than several other well-known entanglement criteria (the fidelity criterion, violation of Mermin-type separability inequalities, the Laskowski-\.Zukowski criterion and the D\"ur-Cirac criterion), and also by showing their great noise robustness for a variety of multiqubit states, including N-qubit GHZ states and Dicke states. Furthermore, for N greater than or equal to 3 they can detect bound entangled states. For all these states, the required number of measurement settings for implementation of the entanglement criteria is shown to be only N+1. If one chooses the familiar Pauli matrices as single-qubit observables, the inequalities take the form of bounds on the anti-diagonal matrix elements of a state in terms of its diagonal matrix elements.Comment: 25 pages, 3 figures. v4: published versio

Uncertainty in prediction and in inference

The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close re-lationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in infer-ence can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this dis-tance leads to a measure of the distinguishability of quantum states, which essentially is the absolute value of the matrix element between the states. The importance of this result to the quantum mechanical uncertainty prin-ciple is noted. The second part of the paper provides a derivation of the statistical distance on basis of the so-called method of support

Two new kinds of uncertainty relations

We review a statistical-geometrical and a generalized entropic approach to the uncertainty principle. Both approaches provide a strengthening and generalization of the standard Heisenberg uncertainty relations, but in different directions