scholarly journals Simulation of Quantum Dynamics Based on the Quantum Stochastic Differential Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ming Li
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Computational Cost ◽  
Quantum Master Equation ◽  
Level System ◽  
Quantum Stochastic Differential Equation ◽  
State Diffusion ◽  
Quantum State Diffusion

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

Primary state diffusion

1994 ◽  
Vol 447 (1929) ◽  
pp. 189-209 ◽  
Keyword(s):  
Quantum State ◽  
State Vector ◽  
Quantum Dynamics ◽  
Diffusion Theory ◽  
The State ◽  
Classical Dynamics ◽  
State Diffusion ◽  
Quantum State Diffusion ◽  
Spontaneous Localization ◽  
Ordinary Quantum

Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Itô state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז 0 first determines the operator, to within an undetermined universal time constant ז 0 . The second and third conditions put opposing bounds on ז 0 . Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diósi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז 0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.

scholarly journals Pure Gaussian state generation via dissipation: a quantum stochastic differential equation approach

2012 ◽  
Vol 370 (1979) ◽  
pp. 5324-5337 ◽  
Author(s):  
Naoki Yamamoto
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Stochastic Differential Equation ◽  
Cluster State ◽  
Dissipative System ◽  
Complete Characterization ◽  
Gaussian State ◽  
Quantum State Transfer ◽  
Quantum Stochastic Differential Equation ◽  
Gaussian System

Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then, a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.

Quantum Stochastic Differential Equation is Unitarily Equivalent to a Symmetric Boundary Value Problem in Fock Space

1998 ◽  
Vol 01 (02) ◽  
pp. 175-199 ◽  
Author(s):  
Alexander M. Chebotarev
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Stochastic Differential Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Boundary Value ◽  
Weak Limit ◽  
Quantum Stochastic Differential Equation ◽  
Markov Evolution

We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of the Schrödinger equations in Fock space: the strong resolvent limit is unitarily equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitarily equivalent to the symmetric (or Stratonovich) form of QSDE. We also prove that QSDE is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps in phase and amplitude of components of Fock vectors belonging to the range of the resolvent. The corresponding Markov evolution equation (the Lindblad or Markov master equation) is derived from the boundary value problem for the Schrödinger equation.

On the theory and application of one-step numerical schemes for solving quantum stochastic differential equation (QSDE)

2014 ◽  
Vol 07 (03) ◽  
pp. 1450037
Author(s):  
T. O. Akinwumi ◽  
B. J. Adegboyegun
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Numerical Schemes ◽  
Quantum Stochastic Differential Equation ◽  
One Step ◽  
Definition Of ◽  
Convergent Sequences ◽  
Solution Techniques

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

ON THE HAMILTONIAN OPERATOR ASSOCIATED TO SOME QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS

2000 ◽  
Vol 03 (04) ◽  
pp. 483-503 ◽  
Author(s):  
M. GREGORATTI
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Unitary Group ◽  
Open Quantum System ◽  
Hamiltonian Operator ◽  
Stochastic Evolution ◽  
Quantum Stochastic Differential Equation ◽  
Special Cases ◽  
Densely Defined ◽  
Full Domain

We consider the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe the stochastic evolution of an open quantum system together with its environment. We study the (unbounded) Hamiltonian operator generating the unitary group connected, as shown by Frigerio and Maassen, to the solution of the equation. We find a densely defined restriction of the Hamiltonian operator; in some special cases we prove that this restriction is essentially self-adjoint and in one particular case we get the whole Hamiltonian with its full domain.

scholarly journals THE STABILITY OF QUANTUM MARKOV FILTERS

2009 ◽  
Vol 12 (01) ◽  
pp. 153-172 ◽  
Author(s):  
RAMON VAN HANDEL
Keyword(s):  
Differential Equation ◽  
Stochastic Model ◽  
Stochastic Differential Equation ◽  
Initial State ◽  
Rank Condition ◽  
Quantum Stochastic Differential Equation ◽  
Absolutely Continuous ◽  
Finite Dimensional ◽  
Initial States ◽  
The Stability

When are quantum filters asymptotically independent of the initial state? We show that this is the case for absolutely continuous initial states when the quantum stochastic model satisfies an observability condition. When the initial system is finite dimensional, this condition can be verified explicitly in terms of a rank condition on the coefficients of the associated quantum stochastic differential equation.

ENCRYPTION AND DECRYPTION FOR QUANTUM SECRET SHARING PROTOCOL WITH HOT TRAPPED IONS

2008 ◽  
Vol 22 (12) ◽  
pp. 1243-1249 ◽  
Author(s):  
WEN-XING YANG ◽  
AI-XI CHEN
Keyword(s):  
Secret Sharing ◽  
Quantum Dynamics ◽  
Thermal State ◽  
Quantum Secret Sharing ◽  
Entanglement Swapping ◽  
Trapped Ions ◽  
State Diffusion ◽  
Encryption And Decryption ◽  
Efficient Scheme ◽  
Quantum State Diffusion

In this letter, a efficient scheme is proposed for the quantum secret encryption and decryption implementation for quantum secret sharing protocol with trapped ions in thermal motion, in which the effective Hamiltonian does not involve the external degree of freedom and thus the scheme is insensitive to the external state, allowing it to be thermal state. The proposed scheme requires no auxiliary states to assist intermediate atomic transitions and conditional quantum dynamics for quantum phase flip and quantum state diffusion. Besides, secret transmission using entanglement swapping also has been presented.

Sign in / Sign up

Export Citation Format

Share Document