General symmetry in the reduced dynamics of two-level system
arXiv:1902.08714 · doi:10.1140/epjb/e2019-90630-0
Abstract
We study general transformation on the density matrix of two-level system that keeps the expectation value of observable invariant. We introduce a set of generators that yields hermiticity and trace preserving general transformation which casts the transformation into simple form. The general transformation is in general not factorized and not completely positive. Consequently, either the parameter of transformation or the density matrix it acts on needs to be restricted. It can transform the system in the forward and backward direction with regard to its parameter, not as a semigroup in the time translation symmetry of dynamical maps. The general transformation can rotate the Bloch vector circularly or hyperbolically, dilate it or translate it. We apply the general transformation to study the general symmetry of amplitude damping and phase damping in two-level system. We generalize the generators to higher level systems.
arXiv commentAccepted by European Physical Journal B
References in corpus (13)
- Concepts and methods in the theory of open quantum systems
- Dynamics of initially entangled open quantum systems
- Generalized Euler Angle Paramterization for SU(N)
- Quantum Markov Channels for Qubits
- Quantum Mechanics Without State Vectors
- Structure and Parametrization of Generic Stochastic Maps of Density Matrices
- On the Thermal Symmetry of the Markovian Master Equation
- A Note on the correspondence between Qubit Quantum Operations and Special Relativity
- Star-unitary transformations. From dynamics to irreversibility and stochastic behavior
- Compilation of relations for the antisymmetric tensors defined by the Lie algebra cocycles of
- All maps equivalent to a given map, completely positive or not
- Symmetry of bilinear master equations for a quantum oscillator
- Liouville invariance in quantum and classical mechanics