Convexity inequalities for estimating free energy and relative entropy

Bounding generalized relative entropies: Nonasymptotic quantum speed limits

Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of research areas. Remarkably, one of the key information-theoretic quantities is given by the relative entropy, which quantifies how difficult is to tell apart two probability distributions, or even two quantum states. Such a quantity rests at the core of fields like metrology, quantum thermodynamics, quantum communication, and quantum information. Given this broadness of applications, it is desirable to understand how this quantity changes under a quantum process. By considering a general unitary channel, we establish a bound on the generalized relative entropies (Rényi and Tsallis) between the output and the input of the channel. As an application of our bounds, we derive a family of quantum speed limits based on relative entropies. Possible connections between this family with thermodynamics, quantum coherence, asymmetry, and single-shot information theory are briefly discussed.

Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature

This work examines the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat and work that can be realized in current laboratory setups. In contrast to other definitions, it uses only properties of the environment and the measurement outcomes, avoiding references to the "measurement" of the central system's state in any basis. These definitions are consistent with the usual laws of thermodynamics at all temperatures, while never requiring complete projective measurement of the entire system. It is shown that the back action of measurement must be counted as work rather than heat to satisfy the second law. Comparisons are made to quantum jump (unravelling) and transition-probability based definitions, many of which appear as particular limits of the present model. These limits show that our total entropy production is a lower bound on traditional definitions of heat that trace out the measurement device. Examining the master equation approximation to the process at finite measurement rates, we show that most interactions with the environment make the system unable to reach absolute zero. We give an explicit formula for the minimum temperature achievable in repeatedly measured quantum systems. The phenomenon of minimum temperature offers an explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and places a fundamental purity limit on quantum computers.