Related papers: Predictability of measurements
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency…
In statistical thermodynamics the 2nd law is properly spelled out in terms of conditioned probabilities. As such it makes the statement, that `entropy increases with time' without preferring a time direction. In this paper I try to explain…
Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of thermodynamics. A long-standing open problem has…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
In a macroscopic (quantum or classical) Hamiltonian system, we prove the second law of thermodynamics in the forms of the minimum work principle and the law of entropy increase, under the assumption that the initial state is described by a…
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…
Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics. This tutorial focuses on the derivation of the first and second law for closed and open quantum systems far from equilibrium, where…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
The second law of thermodynamics is asymmetric with respect to time as it says that the entropy of the universe must have been lower in the past and will be higher in the future. How this time-asymmetric law arises from the time-symmetric…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…
Bell's inequalities, in the form given by Cerf and Adami, are derived from the combination of the second law of thermodynamics and the Markov postulate. Violations of these inequalities are discussed in terms of the mixing characteristics…
This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of…