We consider a process of parameter estimation in a spin- $j$ system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.We consider a process of parameter estimation in a spin-$j$ system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.

Physical Review AAug 6, 2010112 citations

Quantum criticality

Piers Coleman, A. J. Schofield

arXiv:cond-mat/0503002NatureJan 1, 2005621 citations

Quantum Criticality from Within

ScienceMar 4, 20040 citations

Fisher information approach to nonequilibrium phase transitions in a quantum XXZ spin chain with boundary noise

Ugo Marzolino, Tomaž Prosen

We investigated quantum critical behaviors in the nonequilibrium steady state of a XXZ spin chain with boundary Markovian noise using Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behavior due to a phase transition since all the interaction terms are extensive. Perturbatively, in the noise strength, we found superextensive Fisher information at anisotropy $|\mathrm{\ensuremath{\Delta}}|\ensuremath{\leqslant}1$ and irrational $\frac{arccos\mathrm{\ensuremath{\Delta}}}{\ensuremath{\pi}}$ irrespective of the order of two noncommuting limits, i.e., the thermodynamic limit and the limit of sending $\frac{arccos\mathrm{\ensuremath{\Delta}}}{\ensuremath{\pi}}$ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a nonequilibrium quantum phase transition with a critical phase $|\mathrm{\ensuremath{\Delta}}|\ensuremath{\leqslant}1$. From the nonsuperextensivity of the Fisher information of reduced states, we infer that this nonequilibrium quantum phase transition does not have local order parameters but has nonlocal ones, at least at $|\mathrm{\ensuremath{\Delta}}|=1$. In the nonperturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full-state Fisher information and is superextensive only at $|\mathrm{\ensuremath{\Delta}}|=1$. From the latter result, we derived local order parameters at $|\mathrm{\ensuremath{\Delta}}|=1$ in the nonperturbative case. The existence of critical behavior witnessed by the Fisher information in the phase $|\mathrm{\ensuremath{\Delta}}|<1$ is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy $\mathrm{\ensuremath{\Delta}}$, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.We investigated quantum critical behaviors in the nonequilibrium steady state of a XXZ spin chain with boundary Markovian noise using Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behavior due to a phase transition since all the interaction terms are extensive. Perturbatively, in the noise strength, we found superextensive Fisher information at anisotropy $|\mathrm{\ensuremath{\Delta}}|\ensuremath{\leqslant}1$ and irrational $\frac{arccos\mathrm{\ensuremath{\Delta}}}{\ensuremath{\pi}}$ irrespective of the order of two noncommuting limits, i.e., the thermodynamic limit and the limit of sending $\frac{arccos\mathrm{\ensuremath{\Delta}}}{\ensuremath{\pi}}$ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a nonequilibrium quantum phase transition with a critical phase $|\mathrm{\ensuremath{\Delta}}|\ensuremath{\leqslant}1$. From the nonsuperextensivity of the Fisher information of reduced states, we infer that this nonequilibrium quantum phase transition does not have local order parameters but has nonlocal ones, at least at $|\mathrm{\ensuremath{\Delta}}|=1$. In the nonperturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full-state Fisher information and is superextensive only at $|\mathrm{\ensuremath{\Delta}}|=1$. From the latter result, we derived local order parameters at $|\mathrm{\ensuremath{\Delta}}|=1$ in the nonperturbative case. The existence of critical behavior witnessed by the Fisher information in the phase $|\mathrm{\ensuremath{\Delta}}|<1$ is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy $\mathrm{\ensuremath{\Delta}}$, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.

arXiv:1708.07121Physical review. B./Physical review. BSep 1, 201763 citations

We consider a process of parameter estimation in a spin-

j

system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.