# Critical assessment of two-qubit post-Markovian master equations

@article{Campbell2012CriticalAO, title={Critical assessment of two-qubit post-Markovian master equations}, author={Steve Campbell and Andrea Smirne and L. Mazzola and Nicola Lo Gullo and Bassano Vacchini and Thomas Busch and Mauro Paternostro}, journal={Physical Review A}, year={2012}, volume={85}, pages={032120} }

European Cooperation in Science and Technology (MP1006); Science Foundation Ireland (10/IN.1/I2979); Irish Research Council for Science, Engineering and Technology (Embark initiative (RS/2000/137); Engineering and Physical Sciences Research Council (EP/G004759/1)

## 12 Citations

### Entropy production and correlations in a controlled non-Markovian setting

- PhysicsPhysical Review A
- 2018

We study the relationship between (non-)Markovian evolutions, established correlations, and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the…

### A quantum non-Markovian collision model: incoherent swap case

- Physics
- 2013

We have recently presented a collision-model-based framework to tackle non-Markovian quantum dynamics (Ciccarello et al 2012 arXiv:1207.6554). As a distinctive feature, memory is introduced in a…

### Post-Markovian quantum master equations from classical environment fluctuations.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

It is demonstrated that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation, and that these master equations, even with exponential memory functions, may lead to non- Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

### Quantum Evolution beyond the Markovian Semigroup — Generalizing the Stenholm–Barnett Approach

- MathematicsJournal of Russian Laser Research
- 2018

We provide conditions for the memory kernel governing the time-nonlocal quantum master equation which guarantee that the corresponding dynamical map is completely positive and trace-preserving. This…

### System-environment correlations and Markovian embedding of quantum non-Markovian dynamics

- MathematicsPhysical Review A
- 2018

We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e., the open dynamics is modeled through sequences of unitary interactions between…

### Nonequilibrium quantum bounds to Landauer's principle: Tightness and effectiveness

- Physics
- 2017

We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the…

### Commutativity and the emergence of classical objectivity

- Computer ScienceJournal of Physics Communications
- 2022

This work examines how the ability of a system to redundantly proliferate relevant information about its pointer states is affected when it is coupled to multiple baths and sheds light on the role that commutativity between the various system-bath interaction terms plays when establishing the conditions for classical objectivity to be supported.

### Generalized Master Equations Leading to Completely Positive Dynamics.

- MathematicsPhysical review letters
- 2016

The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes and puts into evidence the nonuniqueness of the relationship arising due to the typical quantum issue of operator ordering.

### Quantum renewal processes

- MathematicsScientific Reports
- 2020

We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace-preserving maps. These dynamics going beyond the Lindblad paradigm…

### Time inhomogeneous quantum dynamical maps

- Mathematics
- 2022

We discuss a wide class of time inhomogeneous quantum evolution which is represented by two-parameter family of completely positive trace-preserving maps. These dynamical maps are constructed as…

## References

SHOWING 1-10 OF 41 REFERENCES

### Non-Markovian dynamics of a qubit

- Mathematics, Physics
- 2006

In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the recently…

### Probing the environment of an inaccessible system by a qubit ancilla

- Physics
- 2010

We study the conditions for probing the environment affecting an inaccessible system by means of continuous interaction and measurements performed only on a probe. The scheme exploits the statistical…

### Non-Markovian behavior of small and large complex quantum systems.

- PhysicsPhysical review letters
- 2011

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors, leading to non-Markovian behavior, even in the limit of infinite environments.

### Entanglement and non-markovianity of quantum evolutions.

- MathematicsPhysical review letters
- 2010

Two different measures of non-markovianity are introduced that exploit the specific traits of quantum correlations and are suitable for opposite experimental contexts when complete tomographic knowledge about the evolution is available and when no information whatsoever is available.

### Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain

- Physics
- 2011

Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment…

### Non-Markovian quantum jumps.

- Physics, MathematicsPhysical review letters
- 2008

This approach is a generalization of the standard Monte Carlo wave function method for Markovian dynamics and provides an efficient unraveling of the ensemble dynamics of open quantum systems that interact with structured reservoirs.

### Completely positive post-Markovian master equation via a measurement approach

- Physics
- 2005

A post-Markovian quantum master equation is derived, which includes bath memory effects via a phenomenologically introduced memory kernel kstd. The derivation uses as a formal tool a probabilistic…

### Optimized dynamical decoupling in a model quantum memory

- PhysicsNature
- 2009

The extension of a treatment to predict qubit decoherence under realistic conditions is extended, yielding strong agreement between experimental data and theory for arbitrary pulse sequences incorporating nonidealized control pulses, demonstrating the robustness of qubit memory error suppression through dynamical decoupling techniques across a variety of qubits.

### Decoherence, einselection, and the quantum origins of the classical

- Physics
- 2003

as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus…