Related papers: No-Signalling Fixes the Hilbert-Space Inner Produc…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
The biorthogonal formalism extends conventional quantum mechanics to the non-Hermitian realm. It has, however, been pointed out that the biorthogonal inner product changes with the scaling of the eigenvectors, an ambiguity whose physical…
Violation of the no-signaling principle may occur in PT-symmetric evolutions, that is, evolutions that stem from Hamiltonians that are symmetric with respect to parity and time-reversal, of bipartite entangled states. The violation can be…
Recently, apparent nonphysical implications of non-Hermitian quantum mechanics (NHQM) have been discussed in the literature. In particular, the apparent violation of the no-signaling theorem, discrimination of nonorthogonal states, and the…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state…
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the…
Non-classical correlations resulting from entangled quantum systems have sparked debates about the compatibility of quantum theory and relativity, and about the right way to think about causation. Key to a causal theory is that superluminal…
Let $\mathcal{H}$ be a linear space equipped with an indefinite inner product $[\cdot, \cdot]$. Denote by $\mathcal{F}_{++}=\{f\in\mathcal{H} \ : \ [f,f]>0\}$ the nonlinear set of positive vectors in $\mathcal{H}$. We demonstrate that the…
In quantum mechanics (formulated, say, in Schr\"{o}dinger picture) only the knowledge of a complete set of observables $\Lambda_j$ enables us to declare the related physical inner product (i.e., the Hilbert-space metric $\Theta$ such that…
Godfrey and Sichelman propose a quantum-inspired framework, legal entanglement, to model coupled legal relations and interpretations, with quantitative proxies for modularity and information cost. We identify a specific technical issue in…
Quantum correlations do not allow signalling, and any operation which may be performed on one system of an entangled pair cannot be detected by measurement of the other system alone. This no-signalling condition limits allowed operations…
A non-Hermitian operator $H$ defined in a Hilbert space with inner product $\langle\cdot|\cdot\rangle$ may serve as the Hamiltonian for a unitary quantum system, if it is $\eta$-pseudo-Hermitian for a metric operator (positive-definite…
As is well known, an external magnetic field in configuration space coupled to a quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector…
The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a…
It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply…
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…
The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds…