Trade-off Between Work and Correlations in Quantum Thermodynamics

Quantum thermodynamics and quantum information are two frameworks for employing quantum mechanical systems for practical tasks, exploiting genuine quantum features to obtain advantages with respect to classical implementations. While appearing disconnected at first, the main resources of these frameworks, work and correlations, have a complicated yet interesting relationship that we examine here. We review the role of correlations in quantum thermodynamics, with a particular focus on the conversion of work into correlations. We provide new insights into the fundamental work cost of correlations and the existence of optimally correlating unitaries, and discuss relevant open problems.Comment: 11 pages, 1 figure

Thermodynamic cost of creating correlations

We investigate the fundamental limitations imposed by thermodynamics for creating correlations. Considering a collection of initially uncorrelated thermal quantum systems, we ask how much classical and quantum correlations can be obtained via a cyclic Hamiltonian process. We derive bounds on both the mutual information and entanglement of formation, as a function of the temperature of the systems and the available energy. While for a finite number of systems there is a maximal temperature allowing for the creation of entanglement, we show that genuine multipartite entanglement---the strongest form of entanglement in multipartite systems---can be created at any temperature when sufficiently many systems are considered. This approach may find applications, e.g. in quantum information processing, for physical platforms in which thermodynamic considerations cannot be ignored.Comment: 17 pages, 3 figures, substantially rewritten with some new result

Determining lower bounds on a measure of multipartite entanglement from few local observables

We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases we show that only a few local measurements are necessary to determine these lower bounds.Comment: 11 pages, 2 figure

Correlations in the generalized bloch picture & applications in entanglement detection and quantum thermodynamics

La tesis doctoral resume generalizaciones posibles de la famosa imagen de Bloch y su correspondencia con los generadores del SU(d). En adicion a la obra establecida, propuestamos una nueva base aplicable a sistemas de n-qudit por uso en la imagen de Bloch. Applicamos la decomposicion de Bloch generalizada al problema de la detección de entrelazamiento multipartito en tres avenidas differentes: Una basa en la multiplicativitad de normas, una basa en la norma del tensor de la correlacion y una basa en bases anticommutativas. Adicionalmente, damos una introducion corta a la termodinámica cuántica. Buscamos unitarios que optimalmente créen correlaciones bajo restricciónes de energía. Vemos que la restricción a matrices circulantes simplifica el problema y encuentramos coneciones con la teoría de uni-estocásticidad y la teoría de mayorización.The thesis summarizes possible generalizations of the well-known Bloch picture and its connections to the generators of the SU(d). In addition to the established work we propose a new basis applicable to n-qudit systems for use in the Bloch picture. We apply the generalized Bloch decomposition to the problem of multipartite entanglement detection in three different approaches: One based on multiplicative norms, one on correlation tensor norms and one on anti-commuting bases. Additionally, we give a brief introduction to quantum thermodynamics. We look for unitaries that create correlations optimally under energy restrictions. We will see that restricting to circulant matrices simplifies this problem and find connection to the theory of unistochasticity as well as majorization theory

Measurements in two bases are sufficient for certifying high-dimensional entanglement

High-dimensional encoding of quantum information provides a promising method of transcending current limitations in quantum communication. One of the central challenges in the pursuit of such an approach is the certification of high-dimensional entanglement. In particular, it is desirable to do so without resorting to inefficient full state tomography. Here, we show how carefully constructed measurements in two bases (one of which is not orthonormal) can be used to faithfully and efficiently certify bipartite high-dimensional states and their entanglement for any physical platform. To showcase the practicality of this approach under realistic conditions, we put it to the test for photons entangled in their orbital angular momentum. In our experimental setup, we are able to verify 9-dimensional entanglement for a pair of photons on a 11-dimensional subspace each, at present the highest amount certified without any assumptions on the state.Comment: 11+14 pages, 2+7 figure

Correlations in the generalized bloch picture & applications in entanglement detection and quantum thermodynamics

La tesis doctoral resume generalizaciones posibles de la famosa imagen de Bloch y su correspondencia con los generadores del SU(d). En adicion a la obra establecida, propuestamos una nueva base aplicable a sistemas de n-qudit por uso en la imagen de Bloch. Applicamos la decomposicion de Bloch generalizada al problema de la detección de entrelazamiento multipartito en tres avenidas differentes: Una basa en la multiplicativitad de normas, una basa en la norma del tensor de la correlacion y una basa en bases anticommutativas. Adicionalmente, damos una introducion corta a la termodinámica cuántica. Buscamos unitarios que optimalmente créen correlaciones bajo restricciónes de energía. Vemos que la restricción a matrices circulantes simplifica el problema y encuentramos coneciones con la teoría de uni-estocásticidad y la teoría de mayorización.The thesis summarizes possible generalizations of the well-known Bloch picture and its connections to the generators of the SU(d). In addition to the established work we propose a new basis applicable to n-qudit systems for use in the Bloch picture. We apply the generalized Bloch decomposition to the problem of multipartite entanglement detection in three different approaches: One based on multiplicative norms, one on correlation tensor norms and one on anti-commuting bases. Additionally, we give a brief introduction to quantum thermodynamics. We look for unitaries that create correlations optimally under energy restrictions. We will see that restricting to circulant matrices simplifies this problem and find connection to the theory of unistochasticity as well as majorization theory