Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames

Following the introduction of the task of reference frame error correction, we show how, by using reference frame alignment with clocks, one can add a continuous Abelian group of transversal logical gates to any error-correcting code. With this we further explore a way of circumventing the no-go theorem of Eastin and Knill, which states that if local errors are correctable, the group of transversal gates must be of finite order. We are able to do this by introducing a small error on the decoding procedure that decreases with the dimension of the frames used. Furthermore, we show that there is a direct relationship between how small this error can be and how accurate quantum clocks can be: the more accurate the clock, the smaller the error; and the no-go theorem would be violated if time could be measured perfectly in quantum mechanics. The asymptotic scaling of the error is studied under a number of scenarios of reference frames and error models. The scheme is also extended to errors at unknown locations, and we show how to achieve this by simple majority voting related error correction schemes on the reference frames. In the Outlook, we discuss our results in relation to the AdS/CFT correspondence and the Page-Wooters mechanism.Comment: 10+35 pages. Also see related work uploaded to the arXiv on the same day; arXiv:1902.0771

What is the probability of a thermodynamical transition?

If the second law of thermodynamics forbids a transition from one state to another, then it is still possible to make the transition happen by using a sufficient amount of work. But if we do not have access to this amount of work, can the transition happen probabilistically? In the thermodynamic limit, this probability tends to zero, but here we find that for finite-sized systems, it can be finite. We compute the maximum probability of a transition or a thermodynamical fluctuation from any initial state to any final state, and show that this maximum can be achieved for any final state which is block-diagonal in the energy eigenbasis. We also find upper and lower bounds on this transition probability, in terms of the work of transition. As a bi-product, we introduce a finite set of thermodynamical monotones related to the thermo-majorization criteria which governs state transitions, and compute the work of transition in terms of them. The trade-off between the probability of a transition, and any partial work added to aid in that transition is also considered. Our results have applications in entanglement theory, and we find the amount of entanglement required (or gained) when transforming one pure entangled state into any other.Comment: 15+6 pages, 7+1 figures V3: Added discussion on heralded probability and relation to fluctuation theorems. V2: Emphasized that X can be any state and that the achievability of our result in the full thermodynamics case, holds only when the target state is block-diagonal in the energy eigenbasi

Entanglement fluctuation theorems

Pure state entanglement transformations have been thought of as irreversible, with reversible transformations generally only possible in the limit of many copies. Here, we show that reversible entanglement transformations do not require processing on the many copy level, but can instead be undertaken on individual systems, provided the amount of entanglement which is produced or consumed is allowed to fluctuate. We derive necessary and sufficient conditions for entanglement manipulations in this case. As a corollary, we derive an equation which quantifies the fluctuations of entanglement, which is formally identical to the Jarzynski fluctuation equality found in thermodynamics. One can also relate a forward entanglement transformation to its reverse process in terms of the entanglement cost of such a transformation, in a manner equivalent to the Crooks relation. We show that a strong converse theorem for entanglement transformations is formally related to the second law of thermodynamics, while the fact that the Schmidt rank of an entangled state cannot increase is related to the third law of thermodynamics. Achievability of the protocols is done by introducing an entanglement battery, a device which stores entanglement and uses an amount of entanglement that is allowed to fluctuate but with an average cost which is still optimal. This allows us to also solve the problem of partial entanglement recovery, and in fact, we show that entanglement is fully recovered. Allowing the amount of consumed entanglement to fluctuate also leads to improved and optimal entanglement dilution protocols.Comment: comments welcome, v2 published versio

The second law of quantum thermodynamics as an equality

We investigate the connection between recent results in quantum thermodynamics and fluctuation relations by adopting a fully quantum mechanical description of thermodynamics. By including a work system whose energy is allowed to fluctuate, we derive a set of equalities which all thermodynamical transitions have to satisfy. This extends the condition for maps to be Gibbs-preserving to the case of fluctuating work, providing a more general characterisation of maps commonly used in the information theoretic approach to thermodynamics. For final states, block diagonal in the energy basis, this set of equalities are necessary and sufficient conditions for a thermodynamical state transition to be possible. The conditions serves as a parent equation which can be used to derive a number of results. These include writing the second law of thermodynamics as an equality featuring a fine-grained notion of the free energy. It also yields a generalisation of the Jarzynski fluctuation theorem which holds for arbitrary initial states, and under the most general manipulations allowed by the laws of quantum mechanics. Furthermore, we show that each of these relations can be seen as the quasi-classical limit of three fully quantum identities. This allows us to consider the free energy as an operator, and allows one to obtain more general and fully quantum fluctuation relations from the information theoretic approach to quantum thermodynamics.Comment: 11+3 pages. V4: Updated to match published version. Discussion of thermo-majorization and implementing arbitary unitaries added. V3: Added funding information. V2: Expanded discussion on relation to fluctuation theorem

Work and reversibility in quantum thermodynamics

It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\rho$ to a final state $\sigma$, and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\rho$ to a thermal state $\sigma$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\sigma$ to its original form $\rho$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition, and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.Comment: 14 page

Quantum many-body systems in thermal equilibrium

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical situations, relevant to condensed matter physics, high energy physics, quantum chemistry and quantum computing, among others. We give a pedagogical overview of some of the most important universal features about the physics and complexity of these states, which have the locality of the Hamiltonian at its core. We focus on mathematically rigorous statements, many of them inspired by ideas and tools from quantum information theory. These include bounds on their correlations, the form of the subsystems, various statistical properties, and the performance of classical and quantum algorithms. We also include a summary of a few of the most important technical tools, as well as some self-contained proofs.Comment: 42 Pages + References, 7 Figures. Parts of these notes were the basis for a lecture series within the "Quantum Thermodynamics Summer School 2021" during August 2021 in Les Diablerets, Switzerlan

Biomarcadores de las formas clínicas de esclerosis múltiple: desarrollo de estrategias personalizadas basadas en perfiles inmunológicos de la vía del interferón de tipo I

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Medicina, Departamento de Microbiología I, leída el 10/04/2013Multiple sclerosis (MS) is a highly heterogeneous disease and to date reliable plasma biomarkers that enable to distinguish among the different clinical forms of MS are lacking. The present work has identified blood biomarkers in 182 subjects (129 MS patients and 53 healthy controls) that were consecutively recruited as two independent cohorts. We found a significant lower expression of dipeptydil peptidase 4 (DPP4) and DPP activity in the plasma of MS patients with respect to healthy controls and DPP activity correlated inversely with clinical disability score in MS. Our results demonstrate that the divergent clinical and histology-based MS forms are associated with distinct profiles of circulating biomarkers, mostly chemokines and growth/angiogenic factors (HGF, Eotaxin/CCL11, MCP-1/CCL2, Rantes/CCL5, EGF, MIP-1β/CCL4, VEGF and FGFb); and with different gene expression levels in PBMCs of patients (CLU, IRF2 and LDLR). Responder patients to type I IFN displayed high levels of plasma IP10 and MCP-1, and a specific expression pattern of IFN stimulated genes.La esclerosis múltiple (EM) es una enfermedad muy heterogénea clínicamente que carece de biomarcadores plasmáticos que distingan entre formas clínicas. Este trabajo ha identificado biomarcadores de EM en sangre periférica en 182 sujetos (129 pacientes con EM y 53 controles sanos) reclutados en dos cohortes consecutivas. La expresión de dipeptidil peptidasa 4 (DPP4) y la actividad DPP están significativamente disminuidas en el plasma de nuestros pacientes con EM con respecto a los controles sanos y la actividad DPP se correlaciona inversamente con la escala de discapacidad clínica en EM. Nuestros resultados demuestran que las fases recurrente-remitente y la progresiva se asocian con distintos perfiles de biomarcadores circulantes, en su mayor parte quimiocinas y factores de crecimiento/angiogénicos (HGF, Eotaxin/CCL11, MCP-1/CCL2, Rantes/CCL5, EGF, MIP-1β/CCL4, VEGF y FGFb); y con diferentes niveles de expresión génica en sus PBMCs (CLU, IRF2 y LDLR). Los pacientes respondedores a IFN de tipo I presentan niveles elevados de IP10 y MCP-1 en plasma, así como una expresión específica de los genes estimulados por IFN.Depto. de Inmunología, Oftalmología y ORLFac. de MedicinaTRUEunpu