Positivity in the presence of initial system-environment correlation

Abstract

The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.

close to the published version. 5 pages, 1 figure

References in corpus (20)

• Open Quantum Systems. An Introduction
• Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
• Completely Positive Maps and Classical Correlations
• Dynamics of initially entangled open quantum systems
• Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation
• Witness for initial system-environment correlations in open system dynamics
• Physical accessibility of non-completely positive maps
• Experimental investigation of initial system-environment correlations via trace distance evolution
• Operational approach to open dynamics and quantifying initial correlations
• Dynamical role of system-environment correlations in non-Markovian dynamics
• Quantum State and Process Tomography of Energy Transfer Systems via Ultrafast Spectroscopy
• Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation
• Linear Assignment Maps for Correlated System-Environment States
• Kraus representation in the presence of initial correlations
• The role of preparation in quantum process tomography
• Purity as a witness for initial system-environment correlations in open-system dynamics
• Mapping the Schrodinger picture of open quantum dynamics
• Relaxation Phenomena in a System of Two Harmonic Oscillators

Cited by in corpus (24)

• Non-Markovian quantum processes: complete framework and efficient characterisation
• Quantum collision models: open system dynamics from repeated interactions
• Quantum stochastic processes and quantum non-Markovian phenomena
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Operational approach to open dynamics and quantifying initial correlations
• A general framework for complete positivity
• An introduction to operational quantum dynamics
• Environmental correlations and Markovian to non-Markovian transitions in collisional models
• Quantum Markov Order
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• Genuine Multipartite Entanglement in Time
• Effects of initial system-environment correlations on open quantum system dynamics and state preparation
• Experimental Demonstration of Instrument-specific Quantum Memory Effects and Non-Markovian Process Recovery for Common-Cause Processes
• Non-Markovian quantum control as coherent stochastic trajectories
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Completely positive maps within the framework of direct-sum decomposition of state space
• Non-Markovianity during quantum Zeno effect
• Entropy bounds for quantum processes with initial correlations
• Causal classification of spatiotemporal quantum correlations
• A weak-coupling master equation for arbitrary initial conditions
• Memory Effects in Quantum Processes
• Multiple entropy production for multitime quantum processes
• Sufficient Conditions and Constraints for Reversing General Quantum Errors
• George Sudarshan and Quantum Dynamics