Optimal Quantum Detection without Disturbance

1. Optimal Quantum Detection without Disturbance Chih-Lung Chou, CYCU & Li-Yi Hsu, NCTS

2. Instead of considering composite quantum systems that consists of non-interacting parts, A. Peres and W. K. Wootters discussed a particular composite quantum system that possesses no nonlocal properties. PRL66, 1119(1991) For instance,

3. They found that the information can be better extracted by doing combined measurements. and likewise define and , by cyclic permutations. i.e., the measurementM can be chosen as:

4. As a result, the average information gain increases from 1.05228 bit(by separate measurements) to 1.36907 bit(by combined measurements) Combined measurementsWIN!

5. However, measurements on the signal states will unavoidably destroy the states at the same time.

6. X Z o o o 120 120 120 Spin-up in z direction : the signal qubit

7. e.g., By performing measurements on , we can infer the state of the signal qubit .

8. Measuring direction Probability of success detection If we detect the signal qubit directly, the optimal probability for Stern-Gerlach measurements is

9. Separate measurements on

10. Combined measurements on define Orthonormal basis

12. Detection strategy (1) (2) If the outcome is f4, make a random guess for the signal qubit. Result: