On the Sharpness and Bias of Quantum Effects

Stanley Gudder

Shen Jun, Wu Junde

Javid Naikoo, Subhashish Banerjee, A. K. Pan +1 more

The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital quantum channels are shown to induce unbiased measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. The effect of bias and sharpness parameters on various quantum correlations and on the energy cost of measurements is discussed. Further, we illustrate the quantum circuit implementation of the two element positive operator-valued measures characterized by the bias and sharpness parameters.

T. Pradhan

Javid Naikoo, Subhashish Banerjee, A. K. Pan +1 more

The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital (non-unital) quantum channels are shown to induce unbiased (biased) measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. Further, the effect of bias and sharpness parameters on the energy cost of a measurement and its interplay with the non-Markovian dynamics is also discussed.

Claudio Fernández, Rolando Rebolledo