Related papers: An alternative proof of Wigner theorem on quantum …
We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
We extend Einstein's hole argument into the quantum domain, and argue that quantum observables for quasiclassical superpositional states of gravitational fields require additional information to be well-defined, namely, relative positions…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
The quantum state of a system of qubits can be represented by a Wigner function on a discrete phase space, each axis of the phase space taking values in a finite field. Within this framework, we show that one can make sense of the notion of…
It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is {\em impossible} to do so if the transformation is anti-linear and…
We extend some results of group representation theory and von Neumann algebras to the quaternionic Hilbert space case, proving the double commutant theorem (whose quaternionic proof requires a different procedure) and extend to the…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
Let $H$ be a complex Hilbert space and let ${\mathcal P}(H)$ be the associated projective space (the set of rank-one projections). Suppose that $\dim H\ge 3$. We prove the following Wigner-type theorem: if $H$ is finite-dimensional, then…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
The notion of entanglement can be naturally extended from quantum-states to the level of general quantum evolutions. This is achieved by considering multi-partite unitary transformations as elements of a multi-partite Hilbert space and then…
It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a…
According to a classical result due to Hudson, the Wigner function of a pure, continuous variable quantum state is non-negative if and only if the state is Gaussian. We have proven an analogous statement for finite-dimensional quantum…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth in https://link.aps.org/doi/10.1103/PhysRevA.104.042211 and https://iopscience.iop.org/article/10.1088/1751-8121/aa852f/meta. Said…
For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on…
In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…