The bizarre microscopic quantum world is exemplified by Schrödinger’s cat, where a quantum mechanical “cat” state is said to be both death and alive simultaneously. This non-classical state is called a quantum coherence. Coherence is at odds with macroscopic realism. Our experience is dominated by thermodynamics, which destroys quantum coherences at our length and time scales.
We decided to study the reverse situation: In the microscopic world, can quantum coherence affect thermodynamics? We have posted a new manuscript titled “Thermodynamics of quantum coherence“.
Thermodynamics of quantum coherence [arXiv:1308.1245]
César A. Rodríguez-Rosario, Thomas Frauenheim, Alán Aspuru-Guzik
Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources. Quantum coherences seem to be a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines, affect the efficiency of quantum transport, lead to violations of Fourier’s law, and can be used to dynamically control the temperature of a state. However, the role of quantum coherence in thermodynamics is not fully understood. Here we show that the relative entropy of a state with quantum coherence with respect to its decohered state captures its deviation from thermodynamic equilibrium. As a result, changes in quantum coherence can lead to a heat flow with no associated temperature, and affect the entropy production rate. From this, we derive a quantum version of the Onsager reciprocal relations that shows that there is a reciprocal relation between thermodynamic forces from coherence and quantum transport. Quantum decoherence can be useful and offers new possibilities of thermodynamic control for quantum transport.
In this paper, we showed that quantum coherences are useful in thermodynamics in an exactly reciprocal manner to the way thermodynamics destroys coherences. This theory suggest that this interplay can lead to improved molecular devices, and to a deeper understanding of energy transport in photosynthesis.The main results of this paper include a generalization of the laws of thermodynamics and of the Onsager reciprocal relations for the quantum regime. These allowed us to interpret quantum coherences as a new thermodynamic resource. This new theory provides a framework to unify previous results on quantum Carnot engines , thermal control by quantum measurements, quantum coherences in photosynthetic complexes and transport in molecular devices.
Vanishing quantum discord is not necessary for completely positive maps
The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment state. We reexamine the connections between complete positivity and quantum discord within two different sets of assumptions about the relevant family of initial states. We present an example of a system-environment state with nonvanishing quantum discord that leads to a completely positive map. This invalidates an earlier claim about the necessity of vanishing quantum discord for completely positive maps. In our final remarks, we discuss the physical validity of each approach.
has been published in Physical Review A! This paper challenges some of the main claims of one of the most cited papers in the quantum discord community. We hope this will lead to fruitful discussion on the subject.
Our paper Positivity in the presence of initial system-environment correlation has been published in Physical Review A!
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.
Our paper Unification of witnessing initial system-environment correlations and witnessing non-Markovianity has appeared in Europhysics Letters. Previously mentioned here.
Our other related paper, titled Dynamical role of system-environment correlations in non-Markovian dynamics has been published as a Physical Review A: Rapid Communitcation. Paper previously mentioned here.
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.
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.