Factor H-Related Proteins 1–5

Noise and disturbance of qubit measurements: An information-theoretic characterization

“…This is in contrast to results showing such measurements to be optimal in other related scenarios: Ref. [13] found them to be optimal with respect to different measures of information gain and disturbance, while Ref. [26] showed that they implement minimally unsharp sequential joint measurements.…”

“…(18) does not hold in general, our simulations showed that it required carefully chosen postmeasurement corrections in order to violate it. In this section we go further and show that it is in fact valid for an interesting class of measurements, in which M is a "Lüders instrument" [25] that updates the state according to the so-called "square-root dynamics" [13], and no further correction is applied (i.e., when one considers Such measurements can be seen as a generalisation of standard projective measurements [25], and correspond to many realistic experimental situations.…”

“…This approach differs conceptually from that of Buscemi et al, which is instead based on the uncertainty in the post-measurement distribution conditioned on the pre-measurement distribution, and is more in line with the approach of Ref. [13]. Another proposal [14], albeit in a slightly different operational setting, combines these approaches, using the conditional entropy to define the noise and the relative entropy to define the disturbance.…”

Derivative of the disturbance with respect to information from quantum measurements

“…This trade-off between information and disturbance is of great interest in establishing the foundations of quantum mechanics and plays an important role in quantum information processing and communication [1] techniques, such as quantum cryptography [2][3][4][5]. Many authors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have therefore discussed this trade-off, using several different formulations. For example, Banaszek [7] found an inequality between the amount of information gained and the size of the state change, whereas Cheong and Lee [20] found one between the amount of information gained and the reversibility of the state change.…”

Allowed region and optimal measurement for information versus disturbance in quantum measurements

“…This feature is not only of great interest to the foundations of quantum mechanics but also plays an important role in quantum information processing and communication [1], such as in quantum cryptography [2][3][4][5]. As a result, the relationship between information and disturbances has been the subject of numerous studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] over many years. Most studies have only discussed the disturbance in terms of the size of the state change.…”