scholarly journals Steering Witness and Steering Criterion of Gaussian States

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 62
Author(s):  
Ruifen Ma ◽  
Taotao Yan ◽  
Dantong Wu ◽  
Xiaofei Qi
Keyword(s):  
Continuous Variable ◽  
Covariance Matrices ◽  
Gaussian States ◽  
Quantum Steering ◽  
Bell Nonlocality ◽  
Definition Of

Quantum steering is an important quantum resource, which is intermediate between entanglement and Bell nonlocality. In this paper, we study steering witnesses for Gaussian states in continuous-variable systems. We give a definition of steering witnesses by covariance matrices of Gaussian states, and then obtain a steering criterion by steering witnesses to detect steerability of any (m+n)-mode Gaussian states. In addition, the conditions for two steering witnesses to be comparable and the optimality of steering witnesses are also discussed.

Deterministic Continuous-Time Signals and Systems

2021 ◽  
pp. 562-598
Author(s):  
Stevan Berber
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Continuous Variable ◽  
Linear Time Invariant ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
Linear Time Invariant Systems ◽  
Definition Of ◽  
Time Invariant

Due to the importance of the concept of independent variable modification, the definition of linear-time-invariant system, and their implications for discrete-time signal processing, Chapter 11 presents basic deterministic continuous-time signals and systems. These signals, expressed in the form of functions and functionals such as the Dirac delta function, are used throughout the book for deterministic and stochastic signal analysis, in both the continuous-time and the discrete-time domains. The definition of the autocorrelation function, and an explanation of the convolution procedure in linear-time-invariant systems, are presented in detail, due to their importance in communication systems analysis and synthesis. A linear modification of the independent continuous variable is presented for specific cases, like time shift, time reversal, and time and amplitude scaling.

Visualizing coherence, Bell-nonlocality and their interrelation for two-qubit X states in quantum steering ellipsoid formalism

2019 ◽  
Vol 18 (5) ◽  
Author(s):  
Huan Yang ◽  
Zhi-Yong Ding ◽  
Wen-Yang Sun ◽  
Fei Ming ◽  
Dong Wang ◽  
...  
Keyword(s):  
Quantum Steering ◽  
Bell Nonlocality

scholarly journals MR-proANP and incident cardiovascular disease in patients with type 2 diabetes with and without heart failure with preserved ejection fraction

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Jesper Jensen ◽  
Morten Schou ◽  
Caroline Kistorp ◽  
Jens Faber ◽  
Tine W. Hansen ◽  
...  
Keyword(s):  
Heart Failure ◽  
Type 2 Diabetes ◽  
Ejection Fraction ◽  
Natriuretic Peptides ◽  
Continuous Variable ◽  
Preserved Ejection Fraction ◽  
Reduced Ejection Fraction ◽  
Increased Risk ◽  
Definition Of

Abstract Background Mid-regional pro-atrial natriuretic peptide (MR-proANP) is a useful biomarker in outpatients with type 2 diabetes (T2D) to diagnose heart failure (HF). Elevated B-type natriuretic peptides are included in the definition of HF with preserved ejection fraction (HFpEF) but little is known about the prognostic value of including A-type natriuretic peptides (MR-proANP) in the evaluation of patients with T2D. Methods We prospectively evaluated the risk of incident cardiovascular (CV) events in outpatients with T2D (n = 806, mean ± standard deviation age 64 ± 10 years, 65% male, median [interquartile range] duration of diabetes 12 [6–17] years, 17.5% with symptomatic HFpEF) according to MR-proANP levels and stratified according to HF-status including further stratification according to a prespecified cut-off level of MR-proANP. Results A total of 126 CV events occurred (median follow-up 4.8 [4.1–5.3] years). An elevated MR-proANP, with a cut-off of 60 pmol/l or as a continuous variable, was associated with incident CV events (p < 0.001). Compared to patients without HF, patients with HFpEF and high MR-proANP (≥ 60 pmol/l; median 124 [89–202] pmol/l) and patients with HF and reduced ejection fraction (HFrEF) had a higher risk of CV events (multivariable model; hazard ratio (HR) 2.56 [95% CI 1.64–4.00] and 3.32 [1.64–6.74], respectively). Conversely, patients with HFpEF and low MR-proANP (< 60 pmol/l; median 46 [32–56] pmol/l) did not have an increased risk (HR 2.18 [0.78–6.14]). Conclusions Patients with T2D and HFpEF with high MR-proANP levels had an increased risk for CV events compared to patients with HFpEF without elevated MR-proANP and compared to patients without HF, supporting the use of MR-proANP in the definition of HFpEF from a prognostic point-of-view.

Continuous-variable Bell nonlocality with biphotons produced by spontaneous parametric down-conversion

2020 ◽  
Vol 101 (4) ◽  
Author(s):  
Jonas B. Araujo ◽  
I. G. da Paz ◽  
Helder A. S. Costa ◽  
Carlos H. S. Vieira ◽  
Marcos Sampaio
Keyword(s):  
Continuous Variable ◽  
Parametric Down Conversion ◽  
Bell Nonlocality ◽  
Down Conversion

scholarly journals Fidelity-based unitary operation-induced quantum correlation for continuous-variable systems

2019 ◽  
Vol 17 (04) ◽  
pp. 1950035
Author(s):  
Liang Liu ◽  
Xiaofei Qi ◽  
Jinchuan Hou
Keyword(s):  
Quantum Correlation ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Gaussian Channel ◽  
Simple Computation ◽  
Gaussian States ◽  
Text Mode ◽  
Computation Formula ◽  
Geometric Measurement ◽  
Thermal States

We propose a measure of nonclassical correlation [Formula: see text] in terms of local Gaussian unitary operations based on square of the fidelity [Formula: see text] for bipartite continuous-variable systems. This quantity is easier to be calculated or estimated and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of [Formula: see text] for any [Formula: see text]-mode Gaussian states is presented and an estimation of [Formula: see text] for any [Formula: see text]-mode Gaussian states is given. For any [Formula: see text]-mode Gaussian states, [Formula: see text] does not increase after performing a local Gaussian channel on the unmeasured subsystem. Comparing [Formula: see text] in scale with other quantum correlations such as Gaussian geometric discord for two-mode symmetric squeezed thermal states reveals that [Formula: see text] is much better in detecting quantum correlations of Gaussian states.

scholarly journals GAUSSIAN GEOMETRIC DISCORD

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1773-1786 ◽  
Author(s):  
GERARDO ADESSO ◽  
DAVIDE GIROLAMI
Keyword(s):  
Quantum Discord ◽  
Gaussian Quadrature ◽  
Continuous Variable ◽  
Upper And Lower Bounds ◽  
Gaussian States ◽  
Physical Constraints ◽  
Geometric Measure ◽  
Classical Correlations ◽  
Qubit States ◽  
Thermal States

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

scholarly journals Entanglement, Purity, and Information Entropies in Continuous Variable Systems

2005 ◽  
Vol 12 (02) ◽  
pp. 189-205 ◽  
Author(s):  
Gerardo Adesso ◽  
Alessio Serafini ◽  
Fabrizio Illuminati
Keyword(s):  
Tomographic Reconstruction ◽  
Continuous Variable ◽  
The State ◽  
Upper And Lower Bounds ◽  
Mixed States ◽  
Gaussian States ◽  
Pure States ◽  
Classical Correlations ◽  
Quantum And Classical Correlations

Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.

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