Related papers: No-Signalling Fixes the Hilbert-Space Inner Produc…

In quantum mechanics, physical states are represented by rays in Hilbert space $\mathscr H$, which is a vector space imbued by an inner product $\langle\,|\,\rangle$, whose physical meaning arises as the overlap $\langle\phi|\psi\rangle$…

Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…

We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear…

The no-signalling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems.…

We present natural (invariant) definite and indefinite scalar products on the N=1 superspace which turns out to carry an inherent Hilbert-Krein structure. We are motivated by supersymmetry in physics but prefer a general mathematical…

As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state,…

It has been shown that local quantum measurements and no-signaling imply quantum correlations (Barnum et al. Phys. Rev. Lett., 104, 140401 (2010)). This entails that superquantum correlations will be superluminaly signaling if we admit the…

The no-signaling principle in quantum mechanics is shown to be a consequence of Gleason non-contextuality and the tensor product structure.

A new class of state transformations that are quantum mechanically prohibited is introduced. These can be seen as the generalization of the universal-NOT transformation which, for all pure inputs state of a given Hilbert space produces pure…

It is shown that quantum mechanics is noncontextual if quantum properties are represented by subspaces of the quantum Hilbert space (as proposed by von Neumann) rather than by hidden variables. In particular, a measurement using an…

In the quantum logic framework we show that the no-signaling box model is a particular type of tensor product of the logics of single boxes. Such notion of tensor product is too strong to apply in the category of logics of quantum…

PT-symmetric quantum mechanics, the extension of conventional quantum mechanics to the non-Hermitian Hamiltonian invariant under the combined parity (P) and time reversal (T) symmetry, has been successfully applied to a variety of fields…

In superspace a realization of sl2 is generated by the super Laplace operator and the generalized norm squared. In this paper, an inner product on superspace for which this representation is skew-symmetric is considered. This inner product…

Working within the framework of parity-time-symmetric quantum mechanics we look into the possibility of entanglement generation and demonstrate that the feature of non-violation of no-signaling principle may hold for the simplest…

This work presents a rigorous characterization of inner products on the Hilbert space $S_2$ of Hilbert--Schmidt operators. We first deal with a general setting of continuous sesquilinear forms on a Hilbert space $\mathcal H$, and provide a…

We describe a scheme of quantum mechanics in which the Hilbert space and linear operators are only secondary structures of the theory. As primary structures we consider observables, elements of noncommutative algebra, and the physical…

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As…

We analyze the quantization of dynamical systems that do not involve any background notion of space and time. We give a set of conditions for the introduction of an intrinsic time in quantum mechanics. We show that these conditions are a…

Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin…

We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…