Related papers: A universal gap for non-spin quantum control syste…
Problems involving control of large ensmebles of structurally identical dynamical systems, called \emph{ensemble control}, arise in numerous scientific areas from quantum control and robotics to brain medicine. In many of such applications,…
We give a new short proof for the uniqueness of the universal minimal space. The proof holds for the uniqueness of the universal object in every collection of topological dynamical systems closed under taking projective limits and…
Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
Robust quantum control can achieve noise-resilience of quantum systems and quantum technological devices. While the need for noise-resilience grows with the number of fluctuating quantities, and thus typically with the number of qubits,…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…
It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal correspondence of their quantum spectral statistics with random matrix models. We argue…
A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi…
We prove universal lower bounds for discrepancies (i.e. sizes of spectral gaps of averaging operators) of measure-preserving actions of a locally compact group on probability spaces. For example, a locally compact Hausdorff unimodular group…
The simulation of quantum systems has been a key aim of quantum technologies for decades, and the generalisation to open systems is necessary to include physically realistic systems. We introduce an approach for quantum simulations of open…
The spectral gap - the energy difference between the ground state and first excited state - is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, existence of gapped topological spin liquid…
In the global framework of quantum theory the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain…
The canonical theory of quantum gravity in the loop representation can be extended to incorporate topology change, in the simple case that this refers to the creation or annihilation of "minimalist wormholes" in which two points of the…
An experimental study of the applicability of mechanics equations to describing the process of equilibrium establishing in an isolated spin system was performed. The time-reversion effects were used at the experiments. It was demonstrated,…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
An effective theory is constructed for analyzing a generic phase transition between the quantum spin Hall and the insulator phases. Occurrence of degeneracies due to closing of the gap at the transition are carefully elucidated. For systems…
This paper examines the controllability for quantum control systems with SU(1,1) dynamical symmetry, namely, the ability to use some electromagnetic field to redirect the quantum system toward a desired evolution. The problem is formalized…
We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the…