Related papers: Symmetries of quantum evolutions
We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or…
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
In recent years, the traditional notion of symmetry in quantum theory was expanded to so-called generalised or categorical symmetries, which, unlike ordinary group symmetries, may be non-invertible. This appears to be at odds with Wigner's…
Symmetries of both closed and open-system dynamics imply many significant constraints. These generally have instantiations in both classical and quantum dynamics (Noether's theorem, for instance, applies to both sorts of dynamics). We here…
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an…
The aim of this paper is to give a simple, geometric proof of Wigner's theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that…
We pose and resolve a seeming paradox about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator. But Wigner's theorem…
Wigner's theorem asserts that any symmetry of a quantum system is unitary or antiunitary. In this short note we give two proofs based on the geometry of the Fubini-Study metric.
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first…
The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
Quantum mechanical unitarity in our universe is challenged both by the notion of the big bang, in which nothing transforms into something, and the expansion of space, in which something transforms into more something. This motivates the…
The Wigner's friend type of thought experiments manifest the conceptual challenge on how different observers can have consistent descriptions of a quantum measurement event. In this paper, we analyze the extended version of Wigner's friend…
With a choice of boundary conditions for solutions of the Schr\"odinger equation, state vectors and density operators even for closed systems evolve asymmetrically in time. For open systems, standard quantum mechanics consequently predicts…
The basic ingredients of the `consistent histories' approach to quantum theory are a space $\UP$ of `history propositions' and a space $\D$ of `decoherence functionals'. In this article we consider such history quantum theories in the case…
We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure…
According to Wigner theorem, transformations of quantum states which preserve the probabilities are either unitary or antiunitary. This short communication presents an elementary proof of this theorem that significantly departs from the…