Abstract
We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in a strict sense. The superiority of the coherent protocol is due to the fact that it can exploit a geodesic path in Hilbert space, a path that measurement-based protocols cannot follow.
Highlights
We have considered the time required to prepare a system in a pure state under a constraint on the speed of evolution in Hilbert space
We have shown that the fastest measurement-based protocol, defined in the strict sense, takes a time given by equation (6), and the optimal protocol takes a shorter time given by equation (12)
While we expect our results to help elucidate situations in which coherent feedback (CF) is a better choice than measurement-based feedback (MF), we expect that they will help in the design of CF protocols
Summary
Useful in reducing the effects of noise on quantum dynamical systems [1,2,3,4], can be realized in one of two ways: repeatedly measure the system and apply operations conditional on the measurement results [5,6,7,8,9,10,11,12], or couple the system to another quantum system. (a ‘quantum controller’) avoiding the use of measurements [13,14,15,16] This second form of feedback is referred to as coherent feedback (CF). We show that a coherent protocol can extract all the entropy from the target system faster than any measurement-based protocol. The reason for this is that the coherent protocol can follow a more efficient path in the state-space. Since entropy extraction is at the heart of all feedback protocols that regulate a system against noise, this result has profound implications. We expect that the notion of a geodesic, the most efficient path in state-space, will be useful in designing superior continuoustime CF protocols
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