Related papers: Irreversible Quantum Baker Map
It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of…
As one of the most intriguing intrinsic properties of quantum world, quantum superposition provokes great interests in its own generation. Oszmaniec [Phys. Rev. Lett. 116, 110403 (2016)] have proven that though a universal quantum machine…
Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated…
In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Students in quantum mechanics class are taught that the wave function contains all knowable information about an isolated system. Later in the course, this view seems to be contradicted by the mysterious density matrix, which introduces a…
We present two complementary ways in which Saraceno's symmetric version of the quantum baker's map can be written as a shift map on a string of quantum bits. One of these representations leads naturally to a family of quantizations of the…
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…
Quantum Fourier transform is of primary importance in many quantum algorithms. In order to eliminate the destructive effects of decoherence induced by couplings between the quantum system and its environment, we propose a robust scheme for…
We analyze the structure of the subset of states generated by unital completely positive quantum maps, A witness that certifies that a state does not belong to the subset generated by a given map is constructed. We analyse the…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
For a quantum channel (completely positive, trace-preserving map), we prove a generalization to the infinite dimensional case of a result by Baumgartner and Narnhofer. This result is, in a probabilistic language, a decomposition of a…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
The fascinating concept of coherent quantum absorber - which can absorb any photon emitted by another system while maintaining entanglement with that system - has found diverse implications in open quantum system theory and quantum…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
We study the two dual quantum information effects to manipulate the amount of information in quantum computation: hiding and allocation. The resulting type-and-effect system is fully expressive for irreversible quantum computing, including…