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

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

Early death or retransplantation in adults after orthotopic liver transplantation: Can outcome be predicted?

Early, reliable outcome prediction after a liver transplant would help improve organ use by minimizing unnecessary retransplantations. At the same time, early intervention in those cases destined to fail may ameliorate the high morbidity and mortality associated with retransplantation. The purpose of this study was to analyze several parameters that have been identified in the past as being associated with patient and graft outcome, and to try to develop a model that would allow us to make predictions based on data available in the early postoperative period. A total of 148 patients were followed in a prospective, observational study. Graft failure was defined as patient death or retransplantation within 3 months of surgery. Preoperative variables studied included patient demographics, need for life support, presence of ascites, serum bilirubin, serum albumin, prothrombin time, serum creatinine, and the results of the cytotoxic crossmatch. During the first 5 postoperative days, standard measurements included serum transaminases, serum bilirubin, ketone body ratio, prothrombin time, factor V, and serum lactate. Oxygen consumption was measured shortly after surgery, once the patients had rewarmed to 36°C. There were 131 successful transplants (88.5%) and 17 failures (11.5%). Most of the variables studied were found to be associated with outcome (by univariate analysis) at different points in the early postoperative period. However, receiver operating characteristic curve analysis showed that the predictive ability of even the best parameter was not adequate to make decisions on individual patients. Multivariate analysis, using stepwise logistic regression, yielded a model with an overall accuracy of 92.7%. Again, receiver operating characteristic curve analysis suggested that this model did not achieve the discriminating power needed for routine clinical use. We are still not able to accurately predict outcome in the early posttransplant period. We must be very careful when evaluating parameters, or scoring systems, that are said to accomplish this. It is especially important in this era of cost containment, with its renewed pressures to guide therapy based on our perceived understanding of a patient’s future clinical course. © 1994 by Williams & Wilkins

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

Who is in charge? A review and a research agenda on the 'human side' of the circular economy

The adoption of the circular economy (CE) at the firm level has rarely intersected with human resource management (HRM) – here called 'the human side of organizations' – and these two fields remain largely separate areas of knowledge. While the literature on the CE is expanding, discussion of its implementation in organizations is, so far, rare, along with exploration of the necessary alignment of the CE with green human resource management (GHRM). In this article, we extend the state-of-the-art literature on CE business models through the inclusion of the ‘human side’ of such issues. This goal is met by offering an original integrative GHRM framework for organizations developing CE. The theoretical lenses of stakeholders' theory and the resource based view (RBV) form the foundation of this framework, which represents a 'middle range theory'. We underline the practices and dimensions of the links between GHRM and the 'ReSOLVE' CE model. Through an exploration of this integrative framework, we propose a future research agenda along with original research propositions. Furthermore, the middle-range integrated theoretical framework we propose can serve both academics and practitioners in developing understanding of the human resource management (HRM) and change management aspects of the CE