1,721,402 research outputs found
The Wasserstein Distance of Order 1 for Quantum Spin Systems on Infinite Lattices
Full text linkWe propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice Z(d), which we call specific quantum W-1 distance. The proposal is based on the W-1 distance for qudits of De Palma et al. (IEEE Trans Inf Theory 67(10):6627-6643, 2021) and recovers Ornstein's (d) over bar -distance for the quantum states whose marginal states on any finite number of spins are diagonal in the canonical basis. We also propose a generalization of the Lipschitz constant to quantum interactions on Z(d) and prove that such quantum Lipschitz constant and the specific quantum W-1 distance are mutually dual. We prove a new continuity bound for the von Neumann entropy for a finite set of quantum spins in terms of the quantum W-1 distance, and we apply it to prove a continuity bound for the specific von Neumann entropy in terms of the specific quantum W-1 distance for quantum spin systems on Z(d). Finally, we prove that local quantum commuting interactions above a critical temperature satisfy a transportation-cost inequality, which implies the uniqueness of their Gibbs states
I POLIMORFISMI METABOLICI COME CARATTERI COMPLESSI: IMPLICAZIONI PER IL MONITORAGGIO BIOLOGICO E LA VALUTAZIONE DEL RISCHIODE
No full textQuantum Concentration Inequalities
Full text linkWe establish Transportation Cost Inequalities (TCIs) with respect to the quantum Wasserstein distance by introducing quantum extensions of well-known classical methods: First, we generalize the Dobrushin uniqueness condition to prove that Gibbs states of 1D commuting Hamiltonians satisfy a TCI at any positive temperature and provide conditions under which this first result can be extended to non-commuting Hamiltonians. Next, using a non-commutative version of Ollivier’s coarse Ricci curvature, we prove that high temperature Gibbs states of commuting Hamiltonians on arbitrary hypergraphs H= (V, E) satisfy a TCI with constant scaling as O(|V|). Third, we argue that the temperature range for which the TCI holds can be enlarged by relating it to recently established modified logarithmic Sobolev inequalities. Fourth, we prove that the inequality still holds for fixed points of arbitrary reversible local quantum Markov semigroups on regular lattices, albeit with slightly worsened constants, under a seemingly weaker condition of local indistinguishability of the fixed points. Finally, we use our framework to prove Gaussian concentration bounds for the distribution of eigenvalues of quasi-local observables and argue the usefulness of the TCI in proving the equivalence of the canonical and microcanonical ensembles and an exponential improvement over the weak Eigenstate Thermalization Hypothesis
Quantum Optimal Transport with Quantum Channels
No full textWe propose a new generalization to quantum states of the Wasserstein distance, which is a fundamental distance between probability distributions given by the minimization of a transport cost. Our proposal is the first where the transport plans between quantum states are in natural correspondence with quantum channels, such that the transport can be interpreted as a physical operation on the system. Our main result is the proof of a modified triangle inequality for our transport distance. We also prove that the distance between a quantum state and itself is intimately connected with the Wigner-Yanase metric on the manifold of quantum states. We then specialize to quantum Gaussian systems, which provide the mathematical model for the electromagnetic radiation in the quantum regime. We prove that the noiseless quantum Gaussian attenuators and amplifiers are the optimal transport plans between thermal quantum Gaussian states, and that our distance recovers the classical Wasserstein distance in the semiclassical limit
[New molecular indicators for the prevention of tumor and degenerative diseases: anomalous DNA methylation]
No full textDNA methylation is a physiological mechanism regulating both gene expression and genomic stability. Abnormal DNA methylation is observed in neoplastic as well as degenerative disease, and may affect both the whole genome and specific genes. Aberrant DNA methylation has been recently associated to the exposure to carcinogenic chemical compounds. The characterization of DNA methylation abnormalities by modern molecular biology methods may allow the development of new molecular biomarkers of early biological effects
The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
No full textWe prove a generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum Gaussian systems. Such generalization determines the minimum values of linear combinations of the entropies of subsystems associated to arbitrary linear functions of the quadratures, and holds for arbitrary quantum states including the scenario where the entropies are conditioned on a memory quantum system. We apply our result to prove new entropic uncertainty relations with quantum memory, a generalization of the quantum Entropy Power Inequality, and the linear time scaling of the entanglement entropy produced by quadratic Hamiltonians
New lower bounds to the output entropy of multi-mode quantum Gaussian channels
Full text linkWe prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode quantum Gaussian phase contravariant channels among all the input states with an given entropy. This is the first time that this property is proven for a multi-mode channel without restrictions on the input states. A striking consequence of this result is a new lower bound on the output entropy of all the multi-mode quantum Gaussian attenuators and amplifiers in terms of the input entropy. We apply this bound to determine new upper bounds to the communication rates in two different scenarios. The first is classical communication to two receivers with the quantum degraded Gaussian broadcast channel. The second is the simultaneous classical communication, quantum communication and entanglement generation or the simultaneous public classical communication, private classical communication, and quantum key distribution with the Gaussian quantum-limited attenuator.</p
The entropy power inequality with quantum conditioning
Full text linkThe conditional entropy power inequality is a fundamental inequality in information theory, stating that the conditional entropy of the sum of two conditionally independent vector-valued random variables each with an assigned conditional entropy is minimum when the random variables are Gaussian. We prove the conditional entropy power inequality in the scenario where the conditioning system is quantum. The proof is based on the heat semigroup and on a generalization of the Stam inequality in the presence of quantum conditioning. The entropy power inequality with quantum conditioning will be a key tool of quantum information, with applications in distributed source coding protocols with the assistance of quantum entanglement
Quantum Optimal Transport: Quantum Channels and Qubits
No full textThese notes are based on the lectures given by the second author at the School on Optimal Transport on Quantum Structures at Erdös Center in September 2022. The focus of the exposition is on two recently introduced approaches on quantum optimal transport: one based on quantum channels as generalized transport plans, the other based on the notion of Hamming-Wasserstein distance of order 1 on multiple-qubit systems. The material is presented in an elementary manner with a focus on the finite-dimensional setting
Criteri e metodi di controllo periodico dei lavoratori esposti a rischio. Problemi scientifici, e metodologici nella valutazione del ruolo della suscettibilità individuale e patologie preesistenti
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