Bayesian Nagaoka-Hayashi Bound for Multiparameter Quantum-State Estimation Problem

Quantum-enhanced multiparameter estimation in multiarm interferometers

Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation over that achievable by classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript...

Multiparameter Estimation in Networked Quantum Sensors.

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, ...

Bound State Problem Solution

Exact quantum lower bound for grover's problem

One of the most important quantum algorithms ever discovered is Grover’s algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover’s algorithm is exactly optimal. Similar to existing methods for proving lower bounds, we bound the amount of information we can gain from a single oracle query, but we bound this information in terms of angles. T...

A Lower Bound for Quantum Phase Estimation

We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q of Q, as it is for example in Shor’s order finding algorithm. In this setting we will prove a Ω(log 1/ǫ) lower bound for the number of applications of Q1 , Q2 , . . .. This bound is tigh...