scholarly journals Quantum Zeno Dynamics from General Quantum Operations

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 289
Author(s):  
Daniel Burgarth ◽  
Paolo Facchi ◽  
Hiromichi Nakazato ◽  
Saverio Pascazio ◽  
Kazuya Yuasa
Keyword(s):  
General Type ◽  
Quantum Operation ◽  
Adiabatic Evolution ◽  
Quantum Dynamical Semigroup ◽  
Quantum Operations ◽  
Quantum Zeno Dynamics ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Finite Dimensional ◽  
Arbitrary Quantum

We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We obtain a general type of quantum Zeno dynamics, which unifies all known manifestations in the literature as well as describing new types.

scholarly journals Quantum Zeno Effect in Open Quantum Systems

2021 ◽  
Author(s):  
Simon Becker ◽  
Nilanjana Datta ◽  
Robert Salzmann
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Quantum Zeno Effect ◽  
Quantum Dynamical Semigroup ◽  
Open Quantum ◽  
Quantum Operations ◽  
Zeno Effect ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
First Time

AbstractWe prove the quantum Zeno effect in open quantum systems whose evolution, governed by quantum dynamical semigroups, is repeatedly and frequently interrupted by the action of a quantum operation. For the case of a quantum dynamical semigroup with a bounded generator, our analysis leads to a refinement of existing results and extends them to a larger class of quantum operations. We also prove the existence of a novel strong quantum Zeno limit for quantum operations for which a certain spectral gap assumption, which all previous results relied on, is lifted. The quantum operations are instead required to satisfy a weaker property of strong power-convergence. In addition, we establish, for the first time, the existence of a quantum Zeno limit for open quantum systems in the case of unbounded generators. We also provide a variety of physically interesting examples of quantum operations to which our results apply.

scholarly journals A REMARK ON THE STRUCTURE OF SYMMETRIC QUANTUM DYNAMICAL SEMIGROUPS ON VON NEUMANN ALGEBRAS

2002 ◽  
Vol 05 (04) ◽  
pp. 571-579 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
DEBASHISH GOSWAMI
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Type I ◽  
Quantum Dynamical Semigroup ◽  
Von Neumann ◽  
Matrix Algebras ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Quantum Dynamical Semigroups ◽  
Symmetric Quantum

We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with Abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of square of self-adjoint derivations of the von Neumann algebra. This generalizes some of the results obtained by Albeverio, Høegh-Krohn and Olsen1 for the special case of the finite-dimensional matrix algebras. We also study similar questions for a class of quantum dynamical semigroups with unbounded generators.

scholarly journals Nonlinear extension of the quantum dynamical semigroup

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 420
Author(s):  
Jakub Rembieliński ◽  
Paweł Caban
Keyword(s):  
Type Equation ◽  
Solar Neutrinos ◽  
Spin Density Matrix ◽  
Equivalence Of Ensembles ◽  
Quantum Dynamical Semigroup ◽  
Semigroup Property ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Generated Family ◽  
Linearity Condition

In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.

scholarly journals Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup

2021 ◽  
Vol 127 (5) ◽  
Author(s):  
Dariusz Chruściński ◽  
Gen Kimura ◽  
Andrzej Kossakowski ◽  
Yasuhito Shishido
Keyword(s):  
Relaxation Rates ◽  
Quantum Dynamical Semigroup ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Universal Constraint

scholarly journals Structure of block quantum dynamical semigroups and their product systems

2020 ◽  
Vol 23 (01) ◽  
pp. 2050001
Author(s):  
B. V. Rajarama Bhat ◽  
U. Vijaya Kumar
Keyword(s):  
Von Neumann Algebra ◽  
Markov Semigroup ◽  
Map Building ◽  
Quantum Dynamical Semigroup ◽  
Von Neumann ◽  
Quantum Dynamical ◽  
Product Systems ◽  
Dynamical Semigroup ◽  
Quantum Markov Semigroup ◽  
Unit Formula

Paschke’s version of Stinespring’s theorem associates a Hilbert [Formula: see text]-module along with a generating vector to every completely positive map. Building on this, to every quantum dynamical semigroup (QDS) on a [Formula: see text]-algebra [Formula: see text] one may associate an inclusion system [Formula: see text] of Hilbert [Formula: see text]-[Formula: see text]-modules with a generating unit [Formula: see text]. Suppose [Formula: see text] is a von Neumann algebra, consider [Formula: see text], the von Neumann algebra of [Formula: see text] matrices with entries from [Formula: see text]. Suppose [Formula: see text] with [Formula: see text] is a QDS on [Formula: see text] which acts block-wise and let [Formula: see text] be the inclusion system associated to the diagonal QDS [Formula: see text] with the generating unit [Formula: see text] It is shown that there is a contractive (bilinear) morphism [Formula: see text] from [Formula: see text] to [Formula: see text] such that [Formula: see text] for all [Formula: see text] We also prove that any contractive morphism between inclusion systems of von Neumann [Formula: see text]-[Formula: see text]-modules can be lifted as a morphism between the product systems generated by them. We observe that the [Formula: see text]-dilation of a block quantum Markov semigroup (QMS) on a unital [Formula: see text]-algebra is again a semigroup of block maps.

scholarly journals Some Generalised Fixed Point Theorems Applied to Quantum Operations

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 759
Author(s):  
Umar Batsari Yusuf ◽  
Poom Kumam ◽  
Sikarin Yoo-Kong
Keyword(s):  
Fixed Point ◽  
Quantum State ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Quantum States ◽  
Contractive Condition ◽  
Quantum Operation ◽  
Quantum Operations ◽  
Finite Dimensional

In this paper, we consider an order-preserving mapping T on a complete partial b-metric space satisfying some contractive condition. We were able to show the existence and uniqueness of the fixed point of T. In the application aspect, the fidelity of quantum states was used to establish the existence of a fixed quantum state associated to an order-preserving quantum operation. The method we presented is an alternative in showing the existence of a fixed quantum state associated to quantum operations. Our method does not capitalise on the commutativity of the quantum effects with the fixed quantum state(s) (Luders’s compatibility criteria). The Luders’s compatibility criteria in higher finite dimensional spaces is rather difficult to check for any prospective fixed quantum state. Some part of our results cover the famous contractive fixed point results of Banach, Kannan and Chatterjea.

scholarly journals REMARKS ON SUFFICIENT CONDITIONS FOR CONSERVATIVITY OF MINIMAL QUANTUM DYNAMICAL SEMIGROUPS

2005 ◽  
Vol 17 (07) ◽  
pp. 745-768 ◽  
Author(s):  
CHANGSOO BAHN ◽  
CHUL KI KO ◽  
YONG MOON PARK
Keyword(s):  
Sufficient Conditions ◽  
Heavy Ion ◽  
Elliptic Operators ◽  
Heavy Ion Collision ◽  
Quantum Dynamical Semigroup ◽  
Quantum Dynamical ◽  
Dynamical Semigroup ◽  
Quantum Dynamical Semigroups ◽  
Ion Collision

We have obtained sufficient conditions for conservativity of minimal quantum dynamical semigroup by modifying and extending the method used in [1]. Our criterion for conservativity can be considered as a complement to Chebotarev and Fagnola's conditions [1]. In order to show that our conditions are useful, we apply our results to concrete examples (models of heavy ion collision and noncommutative elliptic operators).

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