Abstract The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family of Bell inequalities with N -settings and d outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of d and many measurement settings. Interestingly, we find that the entanglement entropy behaves very differently depending on whether N = 2 or : when N = 2 the entanglement entropy is a monotone function of d and the most non-classical state is far from maximally entangled, whereas when the entanglement entropy is a non-monotone function of d and converges to that of the maximally entangled state in the limit of large d .Abstract The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family of Bell inequalities with N -settings and d outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of d and many measurement settings. Interestingly, we find that the entanglement entropy behaves very differently depending on whether N = 2 or : when N = 2 the entanglement entropy is a monotone function of d and the most non-classical state is far from maximally entangled, whereas when the entanglement entropy is a non-monotone function of d and converges to that of the maximally entangled state in the limit of large d .

arXiv:1506.04331Journal of Physics A Mathematical and TheoreticalFeb 22, 20167 citations

Maximal Rényi Relative Entropy for $α>2$ Maximal Rényi Relative Entropy for $α>2$

Roberto Rubboli

Quantum relative entropies play a fundamental role in quantum information theory. In the classical setting, Rényi relative entropies constitute, up to linear combinations, the most general class of relative entropies, naturally motivating the search for their minimal and maximal quantum extensions. The minimal extension is known to be the reverse sandwiched Rényi relative entropy for $α\in[0,1/2)$ and the sandwiched Rényi relative entropy for $α\geq 1/2$ . In contrast, the maximal extension had previously been identified only for $α\in[0,2]$ , where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for $α>2$ , the maximal extension is given by the $α$ - $z$ Rényi relative entropy with $z=α-1$ . As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic setting.Quantum relative entropies play a fundamental role in quantum information theory. In the classical setting, Rényi relative entropies constitute, up to linear combinations, the most general class of relative entropies, naturally motivating the search for their minimal and maximal quantum extensions. The minimal extension is known to be the reverse sandwiched Rényi relative entropy for $α\in[0,1/2)$ and the sandwiched Rényi relative entropy for $α\geq 1/2$. In contrast, the maximal extension had previously been identified only for $α\in[0,2]$, where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for $α>2$, the maximal extension is given by the $α$-$z$ Rényi relative entropy with $z=α-1$. As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic setting.

quant-pharXiv:2608.01124Aug 4, 20260 citations

Generalized quantum entropies

Adriana Paula Batista dos Santos, R. Silva, J. S. Alcaniz +1 more

Physics Letters AJul 10, 20118 citations

Stationary Schrödinger Equation and Darwin Term from Maximal Entropy Random Walk

M. Faber

We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born rule appears from measurements between equilibrium states in the past and the same equilibrium states in the future. Introducing potentials by the observation that time, in a gravitational field running in different heights with a different speed, MERW respects the rule that all trajectories of the same duration are counted with equal probability. In this way, MERW allows us to derive the Schrödinger equation for a particle in a potential and the Darwin term of the nonrelativistic expansion of the Dirac equation. Finally, we discuss why quantum mechanics cannot be simply a result of MERW, but, due to the many analogies, MERW may pave the way for further understanding.We describe particles in a potential by a special diffusion process, the maximal entropy random walk (MERW) on a lattice. Since MERW originates in a variational problem, it shares the linear algebra of Hilbert spaces with quantum mechanics. The Born rule appears from measurements between equilibrium states in the past and the same equilibrium states in the future. Introducing potentials by the observation that time, in a gravitational field running in different heights with a different speed, MERW respects the rule that all trajectories of the same duration are counted with equal probability. In this way, MERW allows us to derive the Schrödinger equation for a particle in a potential and the Darwin term of the nonrelativistic expansion of the Dirac equation. Finally, we discuss why quantum mechanics cannot be simply a result of MERW, but, due to the many analogies, MERW may pave the way for further understanding.

arXiv:2304.02368ParticlesDec 26, 20230 citations

Quantum Entropies

Fabio Benatti

Theoretical and mathematical physicsJan 1, 20094 citations

Maximal Rényi Relative Entropy for

α>2

α\in[0,1/2)

and the sandwiched Rényi relative entropy for

α\geq 1/2

. In contrast, the maximal extension had previously been identified only for

α\in[0,2]

, where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for

α>2

, the maximal extension is given by the

α

z

Rényi relative entropy with

z=α-1

. As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic setting.