Paper: Unification of witnessing initial system-environment correlations and witnessing non-Markovianity

We have posted yet another paper in the arXiv. It has been some intense weeks lately.

Unification of witnessing initial system-environment correlations and witnessing non-Markovianity

We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open quantum system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial-correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity at an instance of time in open quantum systems.

This paper is related to the previously posted paper.

Paper: Positivity in the presence of initial system-environment correlation

Another subset of collaborators and I have posted a new paper in the arXiv:

Positivity in the presence of initial system-environment correlation

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

This paper was done in collaboration with Kavan Modi and Alán Aspuru-Guzik.

Paper: Dynamical role of system-environment correlations in non-Markovian dynamics

Our new paper has appeared in the arXiv.

Dynamical role of system-environment correlations in non-Markovian dynamics

We analyse the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al., Phys. Rev. Lett. 103, 210401 (2009), we unveil a fundamental connection between non-Markovian behaviour and dynamics of system-environment correlations. We derive an upper bound to the derivative of rate of change of the distinguishability between different states of the system that explicitly depends on the development and establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight on the mechanisms triggering non-Markovian evolution.

In this paper we studied how certain measures of non-Markovianity are related to the development of correlations between a quantum system and its environment. This was a collaboration with Laura Mazzola, Kavan Modi and Mauro Paternostro.

Discord Conference

I was invited to the Quantum Discord conference in Singapore, organized by Kavan Modi of CQT.

This conference last January brought a big part of the community together for the first time. It was very exiting, with a lot of nice informal discussions, and the great food that characterizes Singapore.

Also, there it was announced a blog dedicated solely to Quantum Discord. This is a good resource to follow all the new papers on the subject.

Published Paper: Non-Markovian Open Quantum Systems

Our paper, Non-Markovian Open Quantum Systems: System-Environment Correlations in Dynamical Maps has been published!

Abstract: We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

You can read it for free for the next couple of weeks in: International Journal of Quantum Information Volume: 9, Issues: 7-8 (2011) pp. 1617-1634

A lot of traveling

I’ve been traveling a lot lately, you might have noticed how I have been unable to update the blog frequently. Here is a quick update of where science has taken me.

November

Dresden – There I visited the group of Wanter Strunz. They are experts in open quantum systems and quantum optics, and we had much to discuss about open systems with initial system-environment correlations. Dresden has some stunning architecture.

UlmSusana Huelga invited me to the beautiful city of Ulm. I’m friends with many people in her group, and this was a great opportunity to catch up, and discuss some new research ideas.

December

Hong KongGuanHua Chen invited to Hong Kong University where we worked together on open quantum systems, master equations and quantum transport. Also, during these days, I was able to participate in the CECAM Workshop on Simulating and Modeling Emerging Electronics. This was a fantastic conference where I learned about the challenges of nano-electronics. This was a fun and intense visit. Fun, because Hong Kong is a very fun city to explore, and has amazing food. Intense, because the conference was very productive, with a lot of ideas flying around.

Non-Markovian Open Quantum Systems: System-Environment Correlations in Dynamical Maps

My paper on Non-Markovian Open Quantum systems has been published in the Special Issue of International Journal of Quantum Information (IJQI):

Non-Markovian Open Quantum Systems: System-Environment Correlations in Dynamical Maps

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

This paper is an updated version of my 2008 preprint.

Pretty Lazy

I had written before about the concept of Lazy States.  Questions in non-equilibrium thermodynamics are usually said to be intractable, due to how much they depend on the details of the dynamical equations. We discovered that in quantum non-equilibrium thermodynamics, there was a simple way to separate the role of system-environment states and of the details of their Hamiltonian coupling. For a class of states, $$left[rho^{SE},rho^{S} right]=0$$ , Lazy States, the entropy rate is always zero independent of the interaction Hamiltonian. These Lazy States are rare, which opens the question of how come thermodynamic equilibrium is so common in the universe?

On a new paper in the arXiv titled Almost all states are pretty lazy, Adrian Hutter and Stephanie Wehner, from the Centre for Quantum Technologies in Singapore, tackled exactly this problem. They were able to show that even if states aren’t lazy, almost all states lead to dynamics which is very close to the ones generated by lazy states. Thus, even if systems are away from equilibrium, they cannot be too far away from it. This leads them to conclude that “Almost all states are pretty lazy”.