Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7$ and verify that they are minimal up to $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5$ .Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7$ and verify that they are minimal up to $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5$.

arXiv:quant-ph/9803066Physical Review LettersAug 17, 199884 citations

Optimal quantum measurements

Alexander Semenovich Holevo

Theoretical and Mathematical PhysicsDec 1, 197312 citations

Thermometry of Gaussian quantum systems using Gaussian measurements

Marina F. B. Cenni, Ludovico Lami, Antonio Acín +1 more

We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically, and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This is in contrast to the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while {on/off} photo-detection-like measurements do it for when the temperature tends to zero. Our results therefore pave the way for effective thermometry of Gaussian quantum systems using experimentally realizable measurements .We study the problem of estimating the temperature of Gaussian systems with feasible measurements, namely Gaussian and photo-detection-like measurements. For Gaussian measurements, we develop a general method to identify the optimal measurement numerically, and derive the analytical solutions in some relevant cases. For a class of single-mode states that includes thermal ones, the optimal Gaussian measurement is either Heterodyne or Homodyne, depending on the temperature regime. This is in contrast to the general setting, in which a projective measurement in the eigenbasis of the Hamiltonian is optimal regardless of temperature. In the general multi-mode case, and unlike the general unrestricted scenario where joint measurements are not helpful for thermometry (nor for any parameter estimation task), it is open whether joint Gaussian measurements provide an advantage over local ones. We conjecture that they are not useful for thermal systems, supported by partial analytical and numerical evidence. We further show that Gaussian measurements become optimal in the limit of large temperatures, while {on/off} photo-detection-like measurements do it for when the temperature tends to zero. Our results therefore pave the way for effective thermometry of Gaussian quantum systems using experimentally realizable measurements .

arXiv:2110.02098QuantumJun 23, 202226 citations

Optimal Quantum Measurements

Blake C. Stacey

SpringerBriefs in mathematical physicsJan 1, 20210 citations

Measurement-Disturbance Tradeoff Outperforming Optimal Cloning

Lukas Knips, Jan Dziewior, Anna-Lena K. Hashagen +3 more

One of the characteristic features of quantum mechanics is that every measurement that extracts information about a general quantum system necessarily causes an unavoidable disturbance to the state of this system. A plethora of different approaches has been developed to characterize and optimize this tradeoff. Here, we apply the framework of quantum instruments to investigate the optimal tradeoff and to derive a class of procedures that is optimal with respect to most meaningful measures. We focus our analysis on binary measurements on qubits as commonly used in communication and computation protocols and demonstrate theoretically and in an experiment that the optimal universal asymmetric quantum cloner, albeit ideal for cloning, is not an optimal procedure for measurements and can be outperformed with high significance.One of the characteristic features of quantum mechanics is that every measurement that extracts information about a general quantum system necessarily causes an unavoidable disturbance to the state of this system. A plethora of different approaches has been developed to characterize and optimize this tradeoff. Here, we apply the framework of quantum instruments to investigate the optimal tradeoff and to derive a class of procedures that is optimal with respect to most meaningful measures. We focus our analysis on binary measurements on qubits as commonly used in communication and computation protocols and demonstrate theoretically and in an experiment that the optimal universal asymmetric quantum cloner, albeit ideal for cloning, is not an optimal procedure for measurements and can be outperformed with high significance.

arXiv:1808.07882Aug 23, 20182 citations

Optimal and finite positive operator valued measurements on a finite number

N

of identically prepared systems have recently been presented. With physical realization in mind, we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}7

and verify that they are minimal up to

N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5