Non-Markovian Quantum Probes

Abstract

Abstract. We review the most recent developments in the theory of open quantum systems focusing on situations in which the reservoir memory effects, due to long-lasting and non-negligible correlations between system and environment, play a crucial role. These systems are often referred to as non-Markovian systems. After a brief summary of different measures of non-Markovianity that have been introduced over the last few years we restrict our analysis to the investigation of information flow between system and environment. Within this framework we introduce an important application of non-Markovianity, namely its use as a quantum probe of complex quantum systems. To illustrate this point we consider quantum probes of ultracold gases, spin chains, and trapped ion crystals and show how properties of these systems can be extracted by means of non-Markovianity measures.

Entangled quantum probes for dynamical environmental noise

“…Indeed, characterizing the noise induced by an external complex system is of great relevance in many areas of nanotechnology, as well as in monitoring biological or chemical processes [5][6][7][8]. Besides, it represents a crucial step to design robust quantum protocols resilient to noise [9][10][11][12][13][14].The proper framework to address characterization by quantum probes [15,16], and to design the best working conditions, is given by quantum estimation theory [17], which provides analytical tools to optimize the three building blocks of an estimation strategy: (i) preparation of the probe system in a suitably optimized state, (ii) controlled interaction of the probe with the system for an optimal amount of time t, (iii) measurement of an optimal observable on the probe. Overall, the ultimate precision for any unbiased estimatorγ of a certain parameter γ is bounded by the quantum Cramèr-Rao (CR) theorem, stating that Var(γ) ≥ [M H(γ)] −1 , where M is the number of measurements and H(γ) is the quantum Fisher information (QFI), i.e.…”

On Time-Local Generators of Quantum Evolution

“…a collection of papers in [32] and references therein. See also Haikka and Maniscalco [33] in this volume.…”

Remote sensing and faithful quantum teleportation through non-localized qubits

“…The supra-Ohmic environment frequently describes the effect of the interaction between a charged particle and its electromagnetic field. It should be noted that such engineering of the ohmicity of the spectrum can be implemented experimentally [94], e.g., when simulating the dephasing model in trapped ultracold atoms, as described in Ref. [95].…”