Quantum thermodynamics in a multipartite setting: A resource theory of local Gaussian work extraction for multimode bosonic systems

Quantum thermodynamics can be cast as a resource theory by considering free access to a heat bath, thereby viewing the Gibbs state at a fixed temperature as a free state and hence any other state as a resource. Here, we consider a multipartite scenario where several parties attempt at extracting work locally, each having access to a local heat bath (possibly with a different temperature), assisted with an energy-preserving global unitary. As a specific model, we analyze a collection of harmonic oscillators or a multimode bosonic system. Focusing on the Gaussian paradigm, we construct a reasonable resource theory of local activity for a multimode bosonic system, where we identify as free any state that is obtained from a product of thermal states (possibly at different temperatures) acted upon by any linear-optics (passive Gaussian) transformation. The associated free operations are then all linear-optics transformations supplemented with tensoring and partial tracing. We show that the local Gaussian extractable work (if each party applies a Gaussian unitary, assisted with linear optics) is zero if and only if the covariance matrix of the system is that of a free state. Further, we develop a resource theory of local Gaussian extractable work, defined as the difference between the trace and symplectic trace of the covariance matrix of the system. We prove that it is a resource monotone that cannot increase under free operations. We also provide examples illustrating the distillation of local activity and local Gaussian extractable work.Comment: 22 pages, 5 figures, minor corrections to make it close to the published version, updated list of reference

Entropy-power uncertainty relations : towards a tight inequality for all Gaussian pure states

We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting entropy-power uncertainty relation is equivalent to the entropic formulation of the uncertainty relation due to Bialynicki-Birula and Mycielski, but can be further extended to rotated variables. Hence, based on a reasonable assumption, we give a partial proof of a tighter form of the entropy-power uncertainty relation taking correlations into account and provide extensive numerical evidence of its validity. Interestingly, it implies the generalized (rotation-invariant) Schr\"odinger-Robertson uncertainty relation exactly as the original entropy-power uncertainty relation implies Heisenberg relation. It is saturated for all Gaussian pure states, in contrast with hitherto known entropic formulations of the uncertainty principle.Comment: 15 pages, 5 figures, the new version includes the n-mode cas

Two-boson quantum interference in time

The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beamsplitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as timelike indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.Comment: 12 pages, 9 figure

Majorization ladder in bosonic Gaussian channels

We show the existence of a majorization ladder in bosonic Gaussian channels, that is, we prove that the channel output resulting from the $n\text{th}$ energy eigenstate (Fock state) majorizes the channel output resulting from the $(n\!+\!1)\text{th}$ energy eigenstate (Fock state). This reflects a remarkable link between the energy at the input of the channel and a disorder relation at its output as captured by majorization theory. This result was previously known in the special cases of a pure-loss channel and quantum-limited amplifier, and we achieve here its nontrivial generalization to any single-mode phase-covariant (or -contravariant) bosonic Gaussian channel. The key to our proof is the explicit construction of a column-stochastic matrix that relates the outputs of the channel for any two subsequent Fock states at its input, which is made possible by exploiting a recently found recurrence relation on multiphoton transition probabilities for Gaussian unitaries [M. G. Jabbour and N. J. Cerf, Phys. Rev. Research 3, 043065 (2021)]. We then discuss possible generalizations and implications of our results.Comment: 7 pages, 3 figures, 1 tabl

A central limit theorem for partially distinguishable bosons

The quantum central limit theorem derived by Cushen and Hudson provides the foundations for understanding how subsystems of large bosonic systems evolving unitarily do reach equilibrium. It finds important applications in the context of quantum interferometry, for example, with photons. A practical feature of current photonic experiments, however, is that photons carry their own internal degrees of freedom pertaining to, e.g., the polarization or spatiotemporal mode they occupy, which makes them partially distinguishable. The ensuing deviation from ideal indistinguishability is well known to have observable consequences, for example in relation with boson bunching, but an understanding of its role in bosonic equilibration phenomena is still missing. Here, we generalize the Cushen-Hudson quantum central limit theorem to encompass scenarios with partial distinguishability, implying an asymptotic convergence of the subsystem's reduced state towards a multimode Gaussian state defined over the internal degrees of freedom. While these asymptotic internal states may not be directly accessible, we show that particle number distributions carry important signatures of distinguishability, which may be used to diagnose experimental imperfections in large boson sampling experiments.Comment: 8+2 pages, 2 figure

Strain effects in deformable semiconductors

Mechanical effects play a role in the electronic behavior of semiconductors in various applications. For example, in strain gauges, the piezoresistive effect is responsible for changes of the current with strain while in MOSFET transistors, strained silicon technologies are used for improving the devices' characteristics. However, the effect of the non-uniformities in the stress fields that develop in the electronic devices are rarely taken into account when addressing the strain effect in semiconductors. In this work, we first address from a general viewpoint the couplings between the mechanical and electronic responses in semiconductors and subsequently specialize the general theory to compute the effect of bending on a p-n junction. Adopting the framework of continuum mechanics and thermodynamics, we develop, in the first part, a fully-coupled continuum theory of the finitely deformable semiconductor which involves the mechanical and electrostatic fields as well as the electronic free carriers densities and current. To this end, we make use of the general principles of mechanics, electromagnetism, species transport and thermodynamics. These laws are completed by thermodynamically consistent constitutive relations whose specific form involves results of statistical physics. While usual semiconductor equations are recovered in a generalized form, the various couplings between the three interacting physics ? mechanics, electrostatics and electronics ? are obtained. In particular, the existence of an electronic-induced stress (proportional to the density of free carriers), which to the best of our knowledge was never discussed before, is found in addition to Maxwell stresses. Considering crystalline semiconductors, our model is simplified to small strains and the quantitatively significant coupling is shown to reduce to the effect of strain on the free carriers transport expressed by the generalized drift-diffusion equations. A discussion on the orders of magnitude of the different couplings in the case of silicon allows to consistently neglect the small effects. Motivated by photovoltaic applications, we subsequently apply our general theory to compute the effect of bending on the current-voltage characteristic of a silicon p-n junction. Accounting for the effect of strain on the band edge energy levels, densities of states and electronic mobilities, we solve the electronic transport equation under non-uniform applied strain. Using asymptotic methods, we compute at first order in terms of applied curvature and strain the change in current induced by the bending of the device. A closed form expression of the strain effect shows that it is predominantly the strain state close to the p-n interface that affects the electronic behavior of the device. These results allow to compute the change in dark current of a typical monocrystalline silicon solar cell when subjected to different strain states: changes is dark-current of the order of 20 % are predicted for strains of the order of 0.2 %

Majorization preservation of Gaussian bosonic channels

It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under majorization are transformed into equally comparable passive states by any phase-insensitive Gaussian bosonic channel. Our proof relies on a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another order relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. The consequences of majorization preservation are discussed in the context of the broadcast communication capacity of Gaussian bosonic channels. Because most of our results are independent of the specific nature of the system under investigation, they could be generalized to other quantum systems and Hamiltonians, providing a new tool that may prove useful in quantum information theory and especially quantum thermodynamics.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Prediction of paravalvular leakage after transcatheter aortic valve implantation

Significant paravalvular leakage (PVL) after transcatheter aortic valve implantation (TAVI) is related to patient mortality. Predicting the development of PVL has focused on computed tomography (CT) derived variables but literature targeting CoreValve devices is limited, controversial, and did not make use of standardized echocardiographic methods. The study included 164 consecutive patients with severe aortic stenosis that underwent TAVI with a Medtronic CoreValve system©, with available pre-TAVI CT and pre-discharge transthoracic echocardiography. The predictive value for significant PVL of the CT-derived Agatston score, aortic annulus size and eccentricity, and “cover index” was assessed, according to both echocardiographic Valve Academic Research Consortium (VARC) criteria and angiographic Sellers criteria. Univariate predictors for more than mild PVL were the maximal diameter of the aortic annulus size (for both angiographic and echocardiographic assessment of PVL), cover index (for echocardiographic assessment of PVL only), and Agatston score (for both angiographic and echocardiographic assessment of PVL). The aortic annulus eccentricity index was not predicting PVL. At multivariate analysis, Agatston score was the only independent predictor for both angiographic and echocardiographic assessment of PVL. Agatston score is the only independent predictor of PVL regardless of the used imaging technique for the definition of PVL