Related papers: Uses of a Quantum Master Inequality
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical…
"Quantum mechanics must be regarded as open systems. On one hand, this is due to the fact that, like in classical physics, any realistic system is subjected to a coupling to an uncontrollable environment which influences it in a…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…
The role of the equivalence principle in the context of non-relativistic quantum mechanics and matter wave interferometry, especially atom beam interferometry, will be discussed. A generalised form of the weak equivalence principle which is…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
Quantum retrodiction involves finding the probabilities for various preparation events given a measurement event. This theory has been studied for some time but mainly as an interesting concept associated with time asymmetry in quantum…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given in terms of the matrix perspective of an operator convex function.…
Quantum mechanics dramatically differs from classical physics, allowing for a wide range of genuinely quantum phenomena. The goal of quantum information is to understand information processing from a quantum perspective. In this mindset, it…
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…
We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
Quantum mechanics is 'emergent' if a statistical treatment of large scale phenomena in a locally deterministic theory requires the use of quantum operators. These quantum operators may allow for symmetry transformations that are not present…
We present some basic inequalities between the classical and quantum values of free energy, entropy and mean energy. We investigate the transition from the deterministic case (classical mechanics) to the probabilistic case (quantum…