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Abstract We elucidate the requirements for quantum operations that achieve environment-assisted invariance (envariance), a symmetry of entanglement. While envariance has traditionally been studied within the framework of local unitary operations, we extend the analysis to consider non-unitary local operations. First, we investigate the conditions imposed on operators acting on pure bipartite entanglement to attain envariance. We show that the local operations must take a direct-sum form in their Kraus operator representations, establishing decoherence-free subspaces. Furthermore, we prove that this also holds for the multipartite scenario. As an immediate consequence, we demonstrate that environment-assisted shortcuts to adiabaticity cannot be achieved through non-unitary operations. In addition, we show that the static condition of the eternal black hole in AdS/CFT is violated when the CFTs are coupled to the external baths. 

We derive a general quantum exchange fluctuation theorem for multipartite systems with arbitrary coupling strengths by taking into account the informational contribution of the back-action of the quantum measurements, which contributes to the increase in the von-Neumann entropy of the quantum system. The resulting second law of thermodynamics is tighter than the conventional Clausius inequality. The derived bound is the quantum mutual information of the conditional thermal state, which is a thermal state conditioned on the initial energy measurement. These results elucidate the role of quantum correlations in the heat exchange between multiple subsystems. 

Abstract Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects can be exploited to enhance the rate of quantum evolution. To this end, we compute a suitable version of the quantum speed limit for numerical and analytical examples. We find that the quantum speed limit grows with the strength of the nonlinearity, yet it does not trivially scale with the “degree” of nonlinearity. This is numerically demonstrated for the parametric harmonic oscillator obeying Gross-Pitaevskii and Kolomeisky dynamics, and analytically for expanding boxes under Gross-Pitaevskii dynamics. 

Thermodynamics originated in the need to understand novel technologies developed by the Industrial Revolution. However, over the centuries, the description of engines, refrigerators, thermal accelerators, and heaters has become so abstract that a direct application of the universal statements to real-life devices is everything but straight forward. The recent, rapid development of quantum thermodynamics has taken a similar trajectory, and, e.g., “quantum engines” have become a widely studied concept in theoretical research. However, if the newly unveiled laws of nature are to be useful, we need to write the dictionary that allows us to translate abstract statements of theoretical quantum thermodynamics to physical platforms and working mediums of experimentally realistic scenarios. To assist in this endeavor, this review is dedicated to provide an overview over the proposed and realized quantum thermodynamic devices and to highlight the commonalities and differences of the various physical situations.