Quantum tomography protocols compared with refined error measures
Refined sample complexities from the tomographic rate function
Information Theory
Summary
Quantum tomography is a way to figure out the state of a quantum system by taking measurements. The authors study different protocols for doing this and compare how well they perform using a detailed error measure called the tomographic rate function. They find that even when protocols need about the same number of samples, this rate function can distinguish their performance more precisely. This helps identify which protocols give better error guarantees beyond just sample count.
What this means in practice
- •For quantum computing engineers: Choose tomography protocols with finer error trade-offs for better quantum device calibration.
- •For quantum algorithm developers: Optimize state reconstruction approaches by selecting protocols judged superior by refined error rates, improving algorithm reliability.
Authors
Arick Grootveld, Alexander Maloney, Jason Pollack, Peixue Wu
Abstract
Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.