Fundamentals of Quantum Mechanics in Liouville Space
arXiv:2003.11472 · doi:10.1088/1361-6404/ab9fdd
Abstract
The purpose of this paper is to articulate a coherent and easy-to-understand way of doing quantum mechanics in any finite-dimensional Liouville space, based on the use of Kronecker product and what we have termed the `bra-flipper' operator. One of the greater strengths of the formalism expatiated on here is the striking similarities it bears with Dirac's bra-ket notation. For the purpose of illustrating how the formalism can be effectively employed, we use it to solve a quantum optical master equation for a two-level quantum system and find its Kraus operator sum representation. The paper is addressed to students and researchers with some basic knowledge of linear algebra who want to acquire a deeper understanding of the Liouville space formalism. The concepts are conveyed so as to make the application of the formalism to more complex problems in quantum physics straightforward and unencumbered.
arXiv comment60 pages, 1 table
References in corpus (15)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Making Sense of Non-Hermitian Hamiltonians
- A short introduction to the Lindblad Master Equation
- Biorthogonal Quantum Mechanics
- Quantum Decoherence
- Symmetries and conserved quantities in Lindblad master equations
- Modeling and Control of Quantum Systems: An Introduction
- Finding the Kraus decomposition from a master equation and vice versa
- Simple Derivation of the Lindblad Equation
- Dynamical signatures of molecular symmetries in nonequilibrium quantum transport
- Conditions for strictly purity-decreasing quantum Markovian dynamics
- Solution of the Lindblad Equation in the Kraus Representation
- Repeatability of measurements: Equivalence of hermitian and non-hermitian observables
- Thermodynamics of Quantum Heat Bath
- Understanding light quanta: First quantization of the free electromagnetic field
Cited by in corpus (39)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Noise-induced quantum synchronization
- Non-Hermitian Hamiltonian Deformations in Quantum Mechanics
- Observation of quantum phase-synchronization in a nuclear spin-system
- Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
- Role of Coherence and Degeneracies in Quantum Synchronisation
- Quantum Fokker-Planck Master Equation for Continuous Feedback Control
- Quasiclassical approaches to the generalized quantum master equation
- Unitarity breaking in self-averaging spectral form factors
- Adaptive quantum error mitigation using pulse-based inverse evolutions
- Measurement-Induced Quantum Synchronization and Multiplexing
- Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians
- Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
- Thermodynamics of a minimal algorithmic cooling refrigerator
- Quantum Chaos and Coherence: Random Parametric Quantum Channels
- Limits to Quantum Gate Fidelity from Near-Field Thermal and Vacuum Fluctuations
- Second quantization of open quantum systems in Liouville space
- Exceptional points and exponential sensitivity for periodically driven Lindblad equations
- Phonon-Induced Decoherence in Color-Center Qubits
- Closed forms of the Zassenhaus formula
- On the Liouville-von Neumann equation for unbounded Hamiltonians
- Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
- Fully Collective Superradiant Lasing with Vanishing Sensitivity to Cavity Length Vibrations
- Error suppression in multicomponent cat codes with photon subtraction and teleamplification
- Quantum-imaginarity-based quantum speed limit
- Analytical solution of the open dispersive Jaynes-Cummings model and perturbative analytical solution of the open quantum Rabi model
- Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
- Quantum control for the Zeno effect with noise
- Robustness of the quantum Mpemba effect against state-preparation errors
- Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model
- Numerical implementation of the partial secular approximation and unified master equation in structured open quantum systems
- Transport approach to quantum state tomography
- Exponentially faster preparation of quantum dimers via driven-dissipative stabilization
- Third-quantized master equations as a classical Ornstein-Uhlenbeck process
- Systematic investigation of dynamic nuclear polarization with boron vacancy in hexagonal boron nitride
- Liouville Fock state lattices and potential simulators
- Variational approach to open quantum systems with long-range competing interactions
- Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line
- Purified pseudomode model for nonlinear system-bath interactions