Quantum union bounds for sequential projective measurements

We present two quantum union bounds for sequential projective measurements. These bounds estimate the disturbance accumulation and probability of outcomes when the measurements are performed sequentially. These results are based on a trigonometric representation of quantum states and should have wide application in quantum information theory for information-processing tasks such as communication and state discrimination, and perhaps even in the analysis of quantum algorithms.

Figure 1

The relationship between the states in the $i\mathrm{th}$ measurement.