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Quantum measurement and control science provides a toolkit for implementing quantum information protocols, overcoming noisy operation and minimizing the use of costly quantum resources. The importance of finding optimal measurement and control strategies is revealed in the task of quantum state discrimination, a characteristic feature of quantum mechanics and a primitive for quantum information science and technology.
When a quantum system is prepared in one of two known nonorthogonal quantum states, no measurement can deterministically tell which state the system is in. Two strategies can be applied to discriminate non-orthogonal states efficiently. Unambiguous state discrimination (USD) is strategy that provides a guess which is either correct, or inconclusive [1]. Alternatively, minimum error discrimination (MED) strategy will always provide a conclusive answer, which can sometimes be incorrect [2]. Perfect nonorthogonal state discrimination is still impossible even when multiple copies of the system are available, although different strategies increase the chance of having conclusive (for USD), or correct (for MED) result. Multiple-copy measurement strategies can be either collective, when a single measurement involves all the copies of the system, or local, when each copy of the system is measured separately. The latter can be further divided into fixed, where the measurement applied to each copy is the same, or adaptive, where the measurement on each subsequent copy depends on the outcomes of the previous measurements [3,4].
A multiple-copy MED strategy is defined by its goal of minimizing the average error for fixed resources, i.e. the number of copies of the system. An alternative approach we consider, is to minimize the average resources required, while keeping errors below a given bound [5]. This approach is central for fault-tolerant quantum computing and has been applied to a number of quantum control strategies [6,7]. We call the corresponding state discrimination task the guaranteed bounded error discrimination (GBED) task. Intuitively, one may assume that the multiple-copy strategies optimal for MED would be also optimal for GBED.
We experimentally apply two known local non-adaptive strategies, previously considered for the MED task, to the two-state GBED problem [5]. We then derive and experimentally demonstrate a new local strategy, designed specifically for the GBED task that outperforms other strategies. Moreover, it performs usually better than, and in the regime of small error, scales better than, the theoretical performance of the optimal adaptive strategy for the MED task.
The discovered reversal in the performance of schemes when swapping the task definition from performance-maximization to resource-minimization, is similar to that previously observed in state purification [6], suggesting that this phenomenon is a generic one.
[1] I. D. Ivanovic, Phys. Lett. A 123, 257 (1987).
[2] C. W. Helstrom, Quantum detection and estimation theory (1976).
[3] A. Acín, et al., Phys. Rev. A 71, 032338 (2005).
[4] B. L. Higgins, et al., Phys. Rev. Lett. 103, 220503 (2009).
[5] S. Slussarenko, et al., PRL 118, 030502 (2017).
[6] H. M. Wiseman and J. F. Ralph. New J. Phys. 8, 90 (2006).
[7] J. Combes, et al., Phys. Rev. Lett. 100, 160503 (2008).
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