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We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…

We derive a set of invariants under local unitary transformations for arbitrary dimensional quantum systems. These invariants are given by hyperdeterminants and independent from the detailed pure state decompositions of a given quantum…

Scales of the microworld are defined on the grounds of the hierarchy that can be set up within a well ordered finite or infinite countable set of well ordered sets. Indirect measurements in pure mathematical as well as physical meaning are…

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance)…

In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework…

Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…

We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the…

The problem of understanding quantum mechanics is in large measure the problem of finding appropriate ways of thinking about the spatial and temporal aspects of the physical world. The standard, substantival, set-theoretic conception of…

Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally…

This paper initiates the study of hidden variables from the discrete, abstract perspective of quantum computing. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another, into a…

The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have…

In this paper we discuss Internal Relativity, a recent program to address the problem of quantum gravity. In our approach we change the relationship between spacetime and matter. Currently we view matter as propagating on spacetime.…

Scalar particles--i.e., scalar-field excitations--in de Sitter space exhibit behavior unlike either classical particles in expanding space or quantum particles in flat spacetime. Their energies oscillate forever, and their interactions are…

An emergent theory of quantum measurement arises directly by considering the particular subset of many body wavefunctions that can be associated with classical condensed matter and its interaction with delocalized wavefunctions. This…

Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…

Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…

Stability against perturbation is a highly nontrivial property of quantum systems and is often a requirement to define new phases. In most systems where stability can be rigorously established, only static perturbations are considered;…

Recent theoretical studies have predicted the existence of caustics in many-body quantum dynamics, where they manifest as extended regions of enhanced probability density that obey temporal and spatial scaling relations. Focusing on the…

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for…

Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…