IRIS Scuola Normale Superiorehttps://ricerca.sns.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Tue, 18 Jan 2022 12:57:10 GMT2022-01-18T12:57:10Z10101Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channelshttp://hdl.handle.net/11384/68989Titolo: Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels
Abstract: We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11384/689892017-01-01T00:00:00ZPassive States Optimize the Output of Bosonic Gaussian Quantum Channelshttp://hdl.handle.net/11384/68985Titolo: Passive States Optimize the Output of Bosonic Gaussian Quantum Channels
Abstract: An ordering between the quantum states emerging from a single-mode gauge-covariant bosonic Gaussian channel is proved. Specifically, we show that within the set of input density matrices with the same given spectrum, the element passive with respect to the Fock basis (i.e., diagonal with decreasing eigenvalues) produces an output, which majorizes all the other outputs emerging from the same set. When applied to pure input states, our finding includes as a special case the result of Mari et al., Nat. Comm. 5, 3826 (2014) which implies that the output associated to the vacuum majorizes the others.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/11384/689852016-01-01T00:00:00ZWeak and strong convergence of derivations and stability of flows with respect to MGH convergencehttp://hdl.handle.net/11384/65646Titolo: Weak and strong convergence of derivations and stability of flows with respect to MGH convergence
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11384/656462017-01-01T00:00:00ZGaussian states minimize the output entropy of the one-mode quantum attenuatorhttp://hdl.handle.net/11384/68987Titolo: Gaussian states minimize the output entropy of the one-mode quantum attenuator
Abstract: We prove that Gaussian thermal input states minimize the output von Neumann entropy of the one-mode Gaussian quantum-limited attenuator for fixed input entropy. The Gaussian quantum-limited attenuator models the attenuation of an electromagnetic signal in the quantum regime. The Shannon entropy of an attenuated real-valued classical signal is a simple function of the entropy of the original signal. A striking consequence of energy quantization is that the output von Neumann entropy of the quantum-limited attenuator is no more a function of the input entropy alone. The proof starts from the majorization result of De Palma et al., IEEE Trans. Inf. Theory 62, 2895 (2016), and is based on a new isoperimetric inequality. Our result implies that geometric input probability distributions minimize the output Shannon entropy of the thinning for fixed input entropy. Moreover, our result opens the way to the multimode generalization that permits to determine both the triple trade-off region of the Gaussian quantum-limited attenuator and the classical capacity region of the Gaussian degraded quantum broadcast channel.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/11384/689872017-01-01T00:00:00ZWell-posedness of Lagrangian flows and continuity equations in metric measure spaceshttp://hdl.handle.net/11384/91747Titolo: Well-posedness of Lagrangian flows and continuity equations in metric measure spaces
Sat, 27 Sep 2014 00:00:00 GMThttp://hdl.handle.net/11384/917472014-09-27T00:00:00ZThe Conditional Entropy Power Inequality for Bosonic Quantum Systemshttp://hdl.handle.net/11384/68992Titolo: The Conditional Entropy Power Inequality for Bosonic Quantum Systems
Abstract: We prove the conditional Entropy Power Inequality for Gaussian quantum systems. This fundamental inequality determines the minimum quantum conditional von Neumann entropy of the output of the beam-splitter or of the squeezing among all the input states where the two inputs are conditionally independent given the memory and have given quantum conditional entropies. We also prove that, for any couple of values of the quantum conditional entropies of the two inputs, the minimum of the quantum conditional entropy of the output given by the conditional Entropy Power Inequality is asymptotically achieved by a suitable sequence of quantum Gaussian input states. Our proof of the conditional Entropy Power Inequality is based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the quantum conditional entropy under the heat semigroup evolution. The beam-splitter and the squeezing are the central elements of quantum optics, and can model the attenuation, the amplification and the noise of electromagnetic signals. This conditional Entropy Power Inequality will have a strong impact in quantum information and quantum cryptography. Among its many possible applications there is the proof of a new uncertainty relation for the conditional Wehrl entropy.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11384/689922018-01-01T00:00:00ZThe One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have GaussianMaximizershttp://hdl.handle.net/11384/77711Titolo: The One-Mode Quantum-Limited Gaussian Attenuator and Amplifier Have GaussianMaximizers
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/11384/777112018-01-01T00:00:00ZQuantum Optimal Transport with Quantum Channelshttp://hdl.handle.net/11384/101584.1Titolo: Quantum Optimal Transport with Quantum Channels
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/11384/101584.12021-01-01T00:00:00ZWell-posedness of Lagrangian flows and continuity equations in metric measure spaceshttp://hdl.handle.net/11384/57121Titolo: Well-posedness of Lagrangian flows and continuity equations in metric measure spaces
Abstract: We establish, in a rather general setting, an analogue of DiPerna-Lions
theory on well-posedness of flows of ODE's associated to Sobolev vector fields.
Key results are a well-posedness result for the continuity equation associated
to suitably defined Sobolev vector fields, via a commutator estimate, and an
abstract superposition principle in (possibly extended) metric measure spaces,
via an embedding into $mathbb{R}^infty$.
When specialized to the setting of Euclidean or infinite dimensional (e.g.
Gaussian) spaces, large parts of previously known results are recovered at
once. Moreover, the class of ${sf RCD}(K,infty)$ metric measure spaces object
of extensive recent research fits into our framework. Therefore we provide, for
the first time, well-posedness results for ODE's under low regularity
assumptions on the velocity and in a nonsmooth context.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11384/571212014-01-01T00:00:00ZThe Quantum Wasserstein Distance of Order 1http://hdl.handle.net/11384/107627.1Titolo: The Quantum Wasserstein Distance of Order 1
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/11384/107627.12021-01-01T00:00:00Z