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Register a new userExperimental Detection of the Correlation Renyi Entropy in the Central Spin Model
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We propose and experimentally measure an entropy that quantifies the volume of correlations among qubits. The experiment is carried out on a nearly isolated quantum system composed of a central spin coupled and initially uncorrelated with 15 other spins. Due to the spin-spin interactions, information flows from the central spin to the surrounding ones forming clusters of multi-spin correlations that grow in time. We design a nuclear magnetic resonance experiment that directly measures the amplitudes of the multi-spin correlations and use them to compute the evolution of what we call correlation Renyi entropy. This entropy keeps growing even after the equilibration of the entanglement entropy. We also analyze how the saturation point and the timescale for the equilibration of the correlation Renyi entropy depend on the system size.
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My previous work [arXiv:1902.00977] studied the dynamics of Renyi entanglement entropy $R_alpha$ in local quantum circuits with charge conservation. Initializing the system in a random product state, it was proved that $R_alpha$ with Renyi index $alpha>1$ grows no faster than diffusively (up to a sublogarithmic correction) if charge transport is not faster than diffusive. The proof was given only for qubit or spin-$1/2$ systems. In this note, I extend the proof to qudit systems, i.e., spin systems with local dimension $dge2$.
Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain Hamiltonian with nearest neighbor interactions that presents an entanglement volume scaling law. This non-translational model is contrived to have couplings that force the accumulation of singlet bonds across the half chain. Our result is complementary to the known relation between non-translational invariant, nearest neighbor interacting Hamiltonians and QMA complete problems.
We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This quantum correlation entropy $S^{rm QC}$ is additive over independent systems, is invariant under local unitary operations, measures total nonclassical correlations (vanishing on states with strictly classical correlation), and reduces to the entanglement entropy for bipartite pure states. It quantifies how well a quantum system can be understood via local measurements, and ties directly to non-equilibrium thermodynamics, including representing a lower bound on the quantum part of thermodynamic entropy production. We discuss two other measures of nonclassical correlation to which this entropy is equivalent, and argue that together they provide a unique thermodynamically distinguished measure.
We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem temperature, T1, and the index q in terms of the temperature, T, entropy, S, and heat capacity, C of the reservoir as T1 = T exp(-S/C) and q = 1 - 1/C. In the infinite C limit, irrespective to the value of S, the Boltzmann-Gibbs approach is fully recovered. We apply this framework for the experimental determination of the original temperature of a finite thermostat, T, from the analysis of hadron spectra produced in high energy collisions, by analyzing frequently considered simple models of the quark-gluon plasma.
We calculate very long low- and high-temperature series for the susceptibility $chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $chi^{(5)}$ and six-particle contribution $chi^{(6)}$. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150000 CPU hours on computer clusters. For $chi^{(5)}$ 10000 terms of the series are calculated {it modulo} a single prime, and have been used to find the linear ODE satisfied by $chi^{(5)}$ {it modulo} a prime. A diff-Pade analysis of 2000 terms series for $chi^{(5)}$ and $chi^{(6)}$ confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the $n$-particle components of the susceptibility, up to a small set of ``additional singularities. We find the presence of singularities at $w=1/2$ for the linear ODE of $chi^{(5)}$, and $w^2= 1/8$ for the ODE of $chi^{(6)}$, which are {it not} singularities of the ``physical $chi^{(5)}$ and $chi^{(6)},$ that is to say the series-solutions of the ODEs which are analytic at $w =0$. Furthermore, analysis of the long series for $chi^{(5)}$ (and $chi^{(6)}$) combined with the corresponding long series for the full susceptibility $chi$ yields previously conjectured singularities in some $chi^{(n)}$, $n ge 7$. We also present a mechanism of resummation of the logarithmic singularities of the $chi^{(n)}$ leading to the known power-law critical behaviour occurring in the full $chi$, and perform a power spectrum analysis giving strong arguments in favor of the existence of a natural boundary for the full susceptibility $chi$.
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