Related papers: Irreversible Quantum Baker Map
We investigate linear parabolic maps on the torus. In a generic case these maps are non-invertible and discontinuous. Although the metric entropy of these systems is equal to zero, their dynamics is non-trivial due to folding of the image…
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…
The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the…
In the topos approach to quantum theory, the spectral presheaf plays the role of the state space of a quantum system. We show how a notion of entropy can be defined within the topos formalism using the equivalence between states and…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
The modular multiplication operator, a central subroutine in Shor's factoring algorithm, is shown to be a coherent superposition of two quantum bakers maps when the multiplier is 2. The classical limit of the maps being completely chaotic,…
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex…
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently…
Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
We derive a simple closed form for the matrix elements of the quantum baker's map that shows that the map is an approximate shift in a symbolic representation based on discrete phase space. We use this result to give a formal proof that the…
We investigate the space of quantum operations, as well as the larger space of maps which are positive, but not completely positive. A constructive criterion for decomposability is presented. A certain class of unistochastic operations,…
We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a…
We give a criterion for a positive mapping on the space of operators on a Hilbert space to be indecomposable. We show that this criterion can be applied to two families of positive maps. These families of maps can then be used to form…
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always imply the averaging over the states of the environment. In practice this is…
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in…
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…
A Floquet systems is a periodically driven quantum system. It can be described by a Floquet operator. If this unitary operator has a gap in the spectrum, then one can define associated topological bulk invariants which can either only…
Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate "fractal" [ fractional-dimensional ] phase-space distributions. Because these distributions and their time-reversed twins have zero phase…
Quantum superposition is often phrased as the ability to add state vectors. In practice, however, the physical quantity is a ray (a rank-one projector), so each input specifies only a projector and leaves a gauge freedom in the phases of…