scholarly journals Entanglement dynamics in Rule 54: Exact results and quasiparticle picture

2021 ◽  
Vol 11 (6) ◽  
Author(s):  
Katja Klobas ◽  
Bruno Bertini
Keyword(s):  
Linear Growth ◽  
Von Neumann Entropy ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Rényi Entropies ◽  
Quantum Quenches ◽  
Initial States ◽  
Local Observables ◽  
Quasiparticle Picture ◽  
Renyi Entropies

We study the entanglement dynamics generated by quantum quenches in the quantum cellular automaton Rule 54. We consider the evolution from a recently introduced class of solvable initial states. States in this class relax (locally) to a one-parameter family of Gibbs states and the thermalisation dynamics of local observables can be characterised exactly by means of an evolution in space. Here we show that the latter approach also gives access to the entanglement dynamics and derive exact formulas describing the asymptotic linear growth of all Rényi entropies in the thermodynamic limit and their eventual saturation for finite subsystems. While in the case of von Neumann entropy we recover exactly the predictions of the quasiparticle picture, we find no physically meaningful quasiparticle description for other Rényi entropies. Our results apply to both homogeneous and inhomogeneous quenches.

scholarly journals Monotonicity of the von Neumann Entropy Expressed as a Function of Rényi Entropies

2014 ◽  
Vol 21 (03) ◽  
pp. 1450006 ◽  
Author(s):  
Mark Fannes
Keyword(s):  
Density Matrix ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Integer Order ◽  
Odd Order ◽  
Rényi Entropies ◽  
Even Order ◽  
Renyi Entropies

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d − 1 integer order Rényi entropies, is monotonically increasing in Rényi entropies of even order and decreasing in those of odd order.

scholarly journals Rényi Extrapolation of Shannon Entropy

2003 ◽  
Vol 10 (03) ◽  
pp. 297-310 ◽  
Author(s):  
Karol Życzkowski
Keyword(s):  
Probability Distribution ◽  
Quantum State ◽  
Shannon Entropy ◽  
Upper Bound ◽  
Von Neumann Entropy ◽  
Discrete Probability ◽  
Von Neumann ◽  
Integer Order ◽  
Rényi Entropies ◽  
Renyi Entropies

Relations between Shannon entropy and Rényi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Rényi entropies of order two and three are known, we provide a lower and an upper bound for the Shannon entropy. The average of both bounds provide an explicit extrapolation for this quantity. These results imply relations between the von Neumann entropy of a mixed quantum state, its linear entropy and traces.

scholarly journals ENTANGLEMENT DYNAMICS IN FINITE QUDIT CHAIN IN CONSISTENT MAGNETIC FIELD

2012 ◽  
Vol 10 (06) ◽  
pp. 1250068 ◽  
Author(s):  
E. A. IVANCHENKO
Keyword(s):  
Magnetic Field ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Magnetic Field Modulation ◽  
Entanglement Measures ◽  
Analytical Formulae ◽  
Initial States ◽  
Von Neumann Equation ◽  
Field Modulation ◽  
The Magnetic Field

Based on the Liouville–von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains from two to six qutrits or three quartits are presented.

scholarly journals Approximations for von Neumann and Renyi entropies of graphs using the Euler-Maclaurin formula

2018 ◽  
Vol 48 ◽  
pp. 227-242
Author(s):  
Natália Bebiano ◽  
Susana Furtado ◽  
João da Providência ◽  
Wei-Ru Xu ◽  
João P. da Providência
Keyword(s):  
Von Neumann ◽  
Rényi Entropies ◽  
Maclaurin Formula ◽  
Renyi Entropies

scholarly journals Note on von Neumann and Rényi entropies of a graph

2017 ◽  
Vol 521 ◽  
pp. 240-253 ◽  
Author(s):  
Michael Dairyko ◽  
Leslie Hogben ◽  
Jephian C.-H. Lin ◽  
Joshua Lockhart ◽  
David Roberson ◽  
...  
Keyword(s):  
Von Neumann ◽  
Rényi Entropies ◽  
Renyi Entropies

scholarly journals The structure of Rényi entropic inequalities

2013 ◽  
Vol 469 (2158) ◽  
pp. 20120737 ◽  
Author(s):  
Noah Linden ◽  
Milán Mosonyi ◽  
Andreas Winter
Keyword(s):  
Quantum State ◽  
Probability Distributions ◽  
Negative Numbers ◽  
Entropic Inequalities ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Universal Inequalities ◽  
Homogeneous Relation ◽  
Rényi Entropies ◽  
Renyi Entropies

We investigate the universal inequalities relating the α -Rényi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropies ( α =1), which are known to satisfy several non-trivial inequalities such as strong subadditivity. Somewhat surprisingly, we find for 0< α <1 that the only inequality is non-negativity: in other words, any collection of non-negative numbers assigned to the non-empty subsets of n parties can be arbitrarily well approximated by the α -entropies of the 2 n −1 marginals of a quantum state. For α >1, we show analogously that there are no non-trivial homogeneous (in particular, no linear) inequalities. On the other hand, it is known that there are further, nonlinear and indeed non-homogeneous, inequalities delimiting the α -entropies of a general quantum state. Finally, we also treat the case of Rényi entropies restricted to classical states (i.e. probability distributions), which, in addition to non-negativity, are also subject to monotonicity. For α ≠0,1, we show that this is the only other homogeneous relation.

scholarly journals Hydrodynamics of quantum entropies in Ising chains with linear dissipation

2022 ◽  
Author(s):  
Vincenzo Alba ◽  
Federico Carollo
Keyword(s):  
Mutual Information ◽  
Hydrodynamic Limit ◽  
Transverse Field ◽  
Quantum Correlations ◽  
Von Neumann Entropy ◽  
Simple Description ◽  
Von Neumann ◽  
Long Time ◽  
Dynamics Of Correlations ◽  
Quasiparticle Picture

Abstract We study the dynamics of quantum information and of quantum correlations after a quantum quench, in transverse field Ising chains subject to generic linear dissipation. As we show, in the hydrodynamic limit of long times, large system sizes, and weak dissipation, entropy-related quantities —such as the von Neumann entropy, the Rényi entropies, and the associated mutual information— admit a simple description within the so-called quasiparticle picture. Specifically, we analytically derive a hydrodynamic formula, recently conjectured for generic noninteracting systems, which allows us to demonstrate a universal feature of the dynamics of correlations in such dissipative noninteracting system. For any possible dissipation, the mutual information grows up to a time scale that is proportional to the inverse dissipation rate, and then decreases, always vanishing in the long time limit. In passing, we provide analytic formulas describing the time-dependence of arbitrary functions of the fermionic covariance matrix, in the hydrodynamic limit.

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