Sharif Digital Repository

We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: (i) The classical part associated with the Fisher information of the probability distribution of the states contributing to the decomposition, and (ii) the quantum part given by the average quantum Fisher information of the states in this decomposition. Next we use a non-Hermitian extension of a symmetric logarithmic derivative in order to obtain another upper bound on quantum Fisher information, which helps to derive a closed form for the bound in evolutions having the semigroup property. We enhance the extended convexity... 

Estimation of parameters is a pivotal task throughout science and technology. The quantum Cramér-Rao bound provides a fundamental limit of precision allowed to be achieved under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cramér-Rao bound for a fairly large class of open system dynamics, which is governed by a... 

Quantum metrology calculates the ultimate precision of all estimation strategies, measuring what is their root-mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover; namely, we derive an information-theoretic quantum metrology. In this setting, we redefine "Heisenberg bound" and "standard quantum limit" (the usual benchmarks in the quantum estimation theory) and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based...