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

G-Protein coupled receptor signalling in pluripotent stem cell-derived cardiovascular cells: Implications for disease modelling

Human pluripotent stem cell derivatives show promise as an in vitro platform to study a range of human cardiovascular diseases. A better understanding of the biology of stem cells and their cardiovascular derivatives will help to understand the strengths and limitations of this new model system. G-protein coupled receptors (GPCRs) are key regulators of stem cell maintenance and differentiation and have an important role in cardiovascular cell signaling. In this review, we will therefore describe the state of knowledge concerning the regulatory role of GPCRs in both the generation and function of pluripotent stem cell derived-cardiomyocytes, -endothelial, and -vascular smooth muscle cells. We will consider how far the in vitro disease models recapitulate authentic GPCR signaling and provide a useful basis for discovery of disease mechanisms or design of therapeutic strategies

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

A tight uniform continuity bound for the Arimoto-R\'enyi conditional entropy and its extension to classical-quantum states

We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple forms which exist in the literature, since it satisfies two desirable properties of a conditional entropy, namely, the fact that conditioning reduces entropy, and that the associated reduction in uncertainty cannot exceed the information gained by conditioning. Furthermore, it has found interesting applications in various information theoretic tasks such as guessing with side information and sequential decoding. This conditional entropy reduces to the conditional Shannon entropy in the limit $\alpha \to 1$, and this in turn allows us to recover the recently obtained tight uniform continuity bound for the latter from our result. Finally, we apply our result to obtain a tight uniform continuity bound for the conditional $\alpha$-R\'enyi entropy of a classical-quantum state, for $\alpha$ in the same range as above. This again yields the corresponding known bound for the conditional entropy of the state in the limit $\alpha \to 1$.Comment: 23 pages. Changes in v2: new references added and minor corrections to existing reference

Complexity of Gaussian quantum optics with a limited number of non-linearities

It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To do so, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.Comment: 5 pages for the main file, 8 pages for the appendix, 3 figure

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

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

Bosonic autonomous entanglement engines with weak bath coupling are impossible

Entanglement is a fundamental feature of quantum physics and a key resource for quantum communication, computing and sensing. Entangled states are fragile and maintaining coherence is a central challenge in quantum information processing. Nevertheless, entanglement can be generated and stabilised through dissipative processes. In fact, entanglement has been shown to exist in the steady state of certain interacting quantum systems subject solely to incoherent coupling to thermal baths. This has been demonstrated in a range of bi- and multipartite settings using systems of finite dimension. Here we focus on the steady state of infinite-dimensionsional bosonic systems. Specifically, we consider any set of bosonic modes undergoing excitation-number-preserving interactions of arbitrary strength and divided between an arbitrary number of parties that each couple weakly to thermal baths at different temperatures. We show that the steady state is always separable.Comment: 10 pages, 1 figur