Related papers: Locality from the Spectrum
Grassmannian local hidden variables are shown to generate all possible quantum correlations in a bipartite quantum system. Grassmann representation of fermions, common in field theory, opens a related perspective. Although Grassmann hidden…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
One of the main methods for protecting quantum information against decoherence is to encode information in the ground subspace (or the low energy sector) of a Hamiltonian with a large energy gap which penalizes errors from environment. The…
The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known…
It was proposed that the tensor product structure of the Hilbert space is uniquely determined by the Hamiltonian's spectrum, for most finite-dimensional cases satisfying certain conditions. I show that any such method would lead to…
The ultimate precision of any measurement of the temperature of a quantum system is the inverse of the local quantum thermal susceptibility [De Pasquale et al., Nature Communications 7, 12782 (2016)] of the subsystem with whom the…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
A subspace of a multipartite Hilbert space is called \textit{locally indistinguishable} if any orthogonal basis of this subspace cannot be perfectly distinguished by local operations and classical communication. Previously it was shown that…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black…
In this paper we consider general probabilistic theories that pertain to circuits which satisfy two very natural assumptions. We provide a formalism that is local in the following very specific sense: calculations pertaining to any region…
Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this…
The analysis of the dynamics of a material point perfectly constrained to a submanifold of the three-dimensional euclidean space and subjected to a locally conservative force's field, namely a force's field corresponding to a closed but not…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
This article aims to study non-local Lagrangians with an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for them. In…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…