26 Sep 2005 | Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone
Quantum metrology involves using quantum effects to enhance the precision of parameter estimation. The paper presents a general framework that encompasses various strategies for achieving this precision. The typical quantum precision enhancement scales as 1/√N, where N is the number of samples. However, with quantum effects such as entanglement or squeezing, this can be improved to 1/N. The paper shows that the 1/N scaling is the optimal bound for precision in parameter estimation.
The paper discusses different strategies for parameter estimation: classical (CC), quantum (QC), and quantum with quantum measurements (QQ). The CC and CQ strategies have a precision limit of 1/√N, while the QC and QQ strategies achieve 1/N. This means that entanglement at the measurement stage is not necessary for achieving the optimal precision. Instead, sequential protocols can achieve the same precision as quantum strategies by using a single probe multiple times.
The paper also discusses the Heisenberg limit in interferometry, which is the ultimate precision bound for phase measurements. This limit is achieved through entangled or squeezed light or through multiround protocols. The paper shows that the Heisenberg limit is indeed the bound for interferometric precision.
The paper also discusses other quantum metrology protocols, such as quantum frequency standards and quantum-positioning protocols. These protocols use entangled states to enhance the precision of measurements. The paper also shows that the optimal precision bound can be achieved without entangled measurements, by using separable measurements.
The paper concludes that state preparation is the primary factor in boosting the precision of parameter estimation, while entangled measurements are not necessary. A √N precision enhancement can be achieved by using an input state that is entangled on a basis of eigenstates of the generator of the unitary operation, and by measuring a set of projectors on a dual basis. This is related to the fact that entangled states can evolve faster than unentangled configurations using the same resources. Alternatively, a multiround protocol can achieve the same optimal precision at the expense of a larger running time.Quantum metrology involves using quantum effects to enhance the precision of parameter estimation. The paper presents a general framework that encompasses various strategies for achieving this precision. The typical quantum precision enhancement scales as 1/√N, where N is the number of samples. However, with quantum effects such as entanglement or squeezing, this can be improved to 1/N. The paper shows that the 1/N scaling is the optimal bound for precision in parameter estimation.
The paper discusses different strategies for parameter estimation: classical (CC), quantum (QC), and quantum with quantum measurements (QQ). The CC and CQ strategies have a precision limit of 1/√N, while the QC and QQ strategies achieve 1/N. This means that entanglement at the measurement stage is not necessary for achieving the optimal precision. Instead, sequential protocols can achieve the same precision as quantum strategies by using a single probe multiple times.
The paper also discusses the Heisenberg limit in interferometry, which is the ultimate precision bound for phase measurements. This limit is achieved through entangled or squeezed light or through multiround protocols. The paper shows that the Heisenberg limit is indeed the bound for interferometric precision.
The paper also discusses other quantum metrology protocols, such as quantum frequency standards and quantum-positioning protocols. These protocols use entangled states to enhance the precision of measurements. The paper also shows that the optimal precision bound can be achieved without entangled measurements, by using separable measurements.
The paper concludes that state preparation is the primary factor in boosting the precision of parameter estimation, while entangled measurements are not necessary. A √N precision enhancement can be achieved by using an input state that is entangled on a basis of eigenstates of the generator of the unitary operation, and by measuring a set of projectors on a dual basis. This is related to the fact that entangled states can evolve faster than unentangled configurations using the same resources. Alternatively, a multiround protocol can achieve the same optimal precision at the expense of a larger running time.