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Milan Mosonyi - One of the best experts on this subject based on the ideXlab platform.
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Quantum hypothesis testing and the operational interpretation of the Quantum renyi relative entropies
Communications in Mathematical Physics, 2015Co-Authors: Milan Mosonyi, Tomohiro OgawaAbstract:We show that the new Quantum Extension of Renyi’s α-relative entropies, introduced recently by Muller-Lennert et al. (J Math Phys 54:122203, 2013) and Wilde et al. (Commun Math Phys 331(2):593–622, 2014), have an operational interpretation in the strong converse problem of Quantum hypothesis testing. Together with related results for the direct part of Quantum hypothesis testing, known as the Quantum Hoeffding bound, our result suggests that the operationally relevant definition of the Quantum Renyi relative entropies depends on the parameter α: for α < 1, the right choice seems to be the traditional definition $${{D_\alpha^{(old)}} (\rho \| \sigma) :=\frac{1}{\alpha-1} \,\,{\rm log\,\,Tr}\,\, \rho^{\alpha} \sigma^{1-\alpha}}$$ , whereas for α > 1 the right choice is the newly introduced version $${D_\alpha^{(new)}} (\rho \| \sigma) := \frac{1}{\alpha-1}\,{\rm log\,\,Tr}\,\big(\sigma^{\frac{1-\alpha}{2 \alpha}}\rho \sigma^{\frac{1-\alpha}{2 \alpha}}\big)^{\alpha}$$ .On the way to proving our main result, we show that the new Renyi α-relative entropies are asymptotically attainable by measurements for α > 1. From this, we obtain a new simple proof for their monotonicity under completely positive trace-preserving maps.
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Quantum hypothesis testing and the operational interpretation of the Quantum renyi relative entropies
arXiv: Quantum Physics, 2013Co-Authors: Milan Mosonyi, Tomohiro OgawaAbstract:We show that the new Quantum Extension of Renyi's \alpha-relative entropies, introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys. 331, (2014), have an operational interpretation in the strong converse problem of Quantum hypothesis testing. Together with related results for the direct part of Quantum hypothesis testing, known as the Quantum Hoeffding bound, our result suggests that the operationally relevant definition of the Quantum Renyi relative entropies depends on the parameter \alpha: for \alpha 1 the right choice is the newly introduced version. As a sideresult, we show that the new Renyi \alpha-relative entropies are asymptotically attainable by measurements for \alpha>1, and give a new simple proof for their monotonicity under completely positive trace-preserving maps.
Uzan Jean-philippe - One of the best experts on this subject based on the ideXlab platform.
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Bouncing compact objects I: Quantum Extension of the Oppenheimer-Snyder collapse
'IOP Publishing', 2020Co-Authors: Achour, Jibril Ben, Brahma Suddhasattwa, Uzan Jean-philippeAbstract:This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models : if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a Quantum bounce. In the later case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep Quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of Quantum black-to-white hole bounce models.Comment: 20 pages, Published in JCA
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Bouncing compact objects I: Quantum Extension of the Oppenheimer-Snyder collapse
HAL CCSD, 2020Co-Authors: Ben Achour Jibril, Brahma Suddhasattwa, Uzan Jean-philippeAbstract:This article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models : if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a Quantum bounce. In the later case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep Quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of Quantum black-to-white hole bounce models
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Bouncing compact objects II: Effective theory of a pulsating Planck star
HAL CCSD, 2020Co-Authors: Ben Achour Jibril, Uzan Jean-philippeAbstract:This article presents an effective Quantum Extension of the seminal Oppenheimer-Snyder (OS) collapse in which the singularity resolution is modeled using the effective dynamics of the spatially closed loop Quantum cosmology. Using the Israel-Darmois junction conditions, it shows that one can consistently glue this bouncing LQC geometry to the classical vacuum exterior Schwarzschild geometry across a time-like thin-shell. Consistency of the construction leads to several major deviations from the classical OS collapse model. Firstly, no trapped region can form and the bounce occurs always above, or at most at the Schwarzschild radius. Secondly, the bouncing star discussed here admits an IR cut-off, additionally to the UV cut-off and describe therefore a pulsating compact object. Thirdly, the scale at which Quantum gravity effects become non-negligible is encoded in the ratio between the UV cut-off of the Quantum theory and the IR cut-off, which in turn, encodes the minimal energy density $\rho_{\text{min}}$ of the star prior to collapse. This energy density is no more fixed by the mass and maximal radius as in the classical OS model, but is now a free parameter of the model. In the end, while the present model cannot describe a black-to-white hole bounce as initially suggested by the Planck star model, it provides a concrete realization of a pulsating compact object based on LQC techniques. Consistency of the model shows that its regime of applicability is restricted to planckian relics while macroscopic stellar objects are excluded. This first minimal construction should serve as a platform for further investigations in order to explore the physics of bouncing compact objects within the framework of loop Quantum cosmology
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Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
'American Physical Society (APS)', 2020Co-Authors: Ben Achour Jibril, Uzan Jean-philippeAbstract:International audienceThis article presents an effective Quantum Extension of the seminal Oppenheimer-Snyder (OS) collapse in which the singularity resolution is modeled using the effective dynamics of the spatially closed loop Quantum cosmology. Imposing the minimal junction conditions, namely the Israel-Darmois conditions, we glue this bouncing LQC geometry to the classical vacuum exterior Schwarzschild geometry across a time-like thin-shell. Consistency of the construction leads to several major deviations from the classical OS collapse model. Firstly, no trapped region can form and the bounce occurs always above, or at most at the Schwarzschild radius. Secondly, the bouncing star discussed here admits an IR cut-off, additionally to the UV cut-off and corresponds therefore to a pulsating compact object. Thirdly, the scale at which Quantum gravity effects become non-negligible is encoded in the ratio between the UV cut-off of the Quantum theory and the IR cut-off, which in turn, encodes the minimal energy density $\rho_{\text{min}}$ of the star prior to collapse. This energy density is no more fixed by the mass and maximal radius as in the classical OS model, but is now a free parameter of the model. In the end, while the present model cannot describe a black-to-white hole bounce as initially suggested by the Planck star model, it provides a concrete realization of a pulsating compact object based on LQC techniques. Consistency of the model shows that its regime of applicability is restricted to Planckian relics while macroscopic stellar objects are excluded. This first minimal construction should serve as a platform for further investigations in order to explore the physics of bouncing compact objects within the framework of loop Quantum cosmology
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Bouncing compact objects. Part I. Quantum Extension of the Oppenheimer-Snyder collapse
'IOP Publishing', 2020Co-Authors: Ben Achour Jibril, Brahma Suddhasattwa, Uzan Jean-philippeAbstract:International audienceThis article proposes a generalization of the Oppenheimer-Snyder model which describes a bouncing compact object. The corrections responsible for the bounce are parameterized in a general way so as to remain agnostic about the specific mechanism of singularity resolution at play. It thus develops an effective theory based on a thin shell approach, inferring generic properties of such a UV complete gravitational collapse. The main result comes in the form of a strong constraint applicable to general UV models: if the dynamics of the collapsing star exhibits a bounce, it always occurs below, or at most at the energy threshold of horizon formation, so that only an instantaneous trapping horizon may be formed while a trapped region never forms. This conclusion relies solely on i) the assumption of continuity of the induced metric across the time-like surface of the star and ii) the assumption of a classical Schwarzschild geometry describing the (vacuum) exterior of the star. In particular, it is completely independent of the choice of corrections inside the star which leads to singularity-resolution. The present model provides thus a general framework to discuss bouncing compact objects, for which the interior geometry is modeled either by a classical or a Quantum bounce. In the latter case, our no-go result regarding the formation of trapped region suggests that additional structure, such as the formation of an inner horizon, is needed to build consistent models of matter collapse describing black-to-white hole bounces. Indeed, such additional structure is needed to keep Quantum gravity effects confined to the high curvature regime, in the deep interior region, providing thus a new challenge for current constructions of Quantum black-to-white hole bounce models
Tomohiro Ogawa - One of the best experts on this subject based on the ideXlab platform.
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Quantum hypothesis testing and the operational interpretation of the Quantum renyi relative entropies
Communications in Mathematical Physics, 2015Co-Authors: Milan Mosonyi, Tomohiro OgawaAbstract:We show that the new Quantum Extension of Renyi’s α-relative entropies, introduced recently by Muller-Lennert et al. (J Math Phys 54:122203, 2013) and Wilde et al. (Commun Math Phys 331(2):593–622, 2014), have an operational interpretation in the strong converse problem of Quantum hypothesis testing. Together with related results for the direct part of Quantum hypothesis testing, known as the Quantum Hoeffding bound, our result suggests that the operationally relevant definition of the Quantum Renyi relative entropies depends on the parameter α: for α < 1, the right choice seems to be the traditional definition $${{D_\alpha^{(old)}} (\rho \| \sigma) :=\frac{1}{\alpha-1} \,\,{\rm log\,\,Tr}\,\, \rho^{\alpha} \sigma^{1-\alpha}}$$ , whereas for α > 1 the right choice is the newly introduced version $${D_\alpha^{(new)}} (\rho \| \sigma) := \frac{1}{\alpha-1}\,{\rm log\,\,Tr}\,\big(\sigma^{\frac{1-\alpha}{2 \alpha}}\rho \sigma^{\frac{1-\alpha}{2 \alpha}}\big)^{\alpha}$$ .On the way to proving our main result, we show that the new Renyi α-relative entropies are asymptotically attainable by measurements for α > 1. From this, we obtain a new simple proof for their monotonicity under completely positive trace-preserving maps.
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Quantum hypothesis testing and the operational interpretation of the Quantum renyi relative entropies
arXiv: Quantum Physics, 2013Co-Authors: Milan Mosonyi, Tomohiro OgawaAbstract:We show that the new Quantum Extension of Renyi's \alpha-relative entropies, introduced recently by Muller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013), and Wilde, Winter, Yang, Commun. Math. Phys. 331, (2014), have an operational interpretation in the strong converse problem of Quantum hypothesis testing. Together with related results for the direct part of Quantum hypothesis testing, known as the Quantum Hoeffding bound, our result suggests that the operationally relevant definition of the Quantum Renyi relative entropies depends on the parameter \alpha: for \alpha 1 the right choice is the newly introduced version. As a sideresult, we show that the new Renyi \alpha-relative entropies are asymptotically attainable by measurements for \alpha>1, and give a new simple proof for their monotonicity under completely positive trace-preserving maps.
Arleta Szkola - One of the best experts on this subject based on the ideXlab platform.
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THE CHERNOFF LOWER BOUND FOR SYMMETRIC Quantum HYPOTHESIS TESTING
Annals of Statistics, 2009Co-Authors: Michael Nussbaum, Arleta SzkolaAbstract:We consider symmetric hypothesis testing in Quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite Quantum system. We prove a lower bound on the asymptotic rate exponents of Bayesian error probabilities. The bound represents a Quantum Extension of the Chernoff bound, which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set. In our framework, the classical result is reproduced if the two hypothetic density operators commute. Recently, it has been shown elsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is achievable also in the generic Quantum (noncommutative) case. This implies that our result is one part of the definitive Quantum Chernoff bound.
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a lower bound of chernoff type for symmetric Quantum hypothesis testing
2006Co-Authors: Michael Nussbaum, Arleta SzkolaAbstract:We consider symmetric hypothesis testing in Quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite Quantum system. We prove a lower bound on the asymptotic rate exponents of Bayesian error probabilities. The bound represents a Quantum Extension of the Chernoff bound, which gives the best asymptotically achievable error exponent in classical discrimination between two probability measures on a finite set. In our framework, the classical result is reproduced if the two hypothetic density operators commute. Recently, it has been shown elsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is achievable also in the generic Quantum (noncommutative) case. This implies that our result is one part of the definitive Quantum Chernoff bound.
Jerome Daligault - One of the best experts on this subject based on the ideXlab platform.
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collisional transport coefficients of dense high temperature plasmas within the Quantum landau fokker planck framework
Physics of Plasmas, 2018Co-Authors: Jerome DaligaultAbstract:We extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its Quantum Extension that includes Quantum degeneracy effects is valid. To this end, the Quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficients rapidly becomes non-negligible outside the domain of validity of the classical Landau equation. For the electron-ion plasmas, the effect of the Pauli exclusion principle depends sensitively on the ion charge Z and varies non-monotonically with Θ. For instance, for ion charge Z = 1, the electrical conductivity is increased by up to ∼30% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ∼9%, and the shear viscosity coefficient is increased by up to ∼13%. In the Lorentz gas ( Z→∞) limit, the electrical conductivity is reduced by up to ∼14% compared to its classical value over the range of degeneracy parameters studied, the thermal conductivity is reduced by up to ∼39%, and the shear viscosity coefficient is not affected.We extend the long-established formulas for the transport coefficients of classical plasmas inside the dense plasma regime for temperatures and densities where the classical Landau equation breaks down but its Quantum Extension that includes Quantum degeneracy effects is valid. To this end, the Quantum Landau kinetic equation is solved by the Chapman-Enskog method. The mathematical derivation is done in full generality, i.e., for multicomponent systems and to all orders of the polynomials expansion used to approximate the distribution functions. We apply the general results to two important examples, the electron gas model and an electron-ion plasma model consisting of one type of ions of any charge. We discuss the combined effects of the Pauli exclusion principle, of the electron-electron, and of the electron-ion collisions on the transport coefficients and on the convergence of the Chapman-Enskog method. For the electron gas model, the effect of the Pauli exclusion principle on the transport coefficient...
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on the Quantum landau collision operator and electron collisions in dense plasmas
Physics of Plasmas, 2016Co-Authors: Jerome DaligaultAbstract:The Quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include Quantum statistical effects, is discussed. The Quantum Extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the Quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the Quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized Quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the Quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the Quantum Extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the Quantum and classical Landau collision operators are emphasized.
