Randomized truncation of quantum states

Abstract:A fundamental task in quantum information is to approximate a pure quantum state in terms of sparse states or, for a bipartite system, states of bounded Schmidt rank. The optimal deterministic approximation in each case is straightforward, and maximizes the fidelity: keep the largest entries or singular values. On the other hand, random mixtures of sparse states can achieve quadratically improved trace distances, and yield nontrivial bounds on other distance measures like the robustness. In this work, we give efficient algorithms for finding mixtures of sparse states that optimally approximate a given pure state in either trace distance or robustness. These algorithms also yield descriptions of efficiently samplable ensembles of sparse, or less-entangled, states that correspond to these optimal mixed approximations. This can be used for the truncation step of algorithms for matrix product states, improving their accuracy while using no extra memory and no asymptotic increase in runtime, and we demonstrate this improvement numerically. Our proofs rely on tools from convex optimization and zero-sum games, as well as rigorous gurarantees for computing and sampling from maximum-entropy distributions. In particular, a key step in our construction is conditional Poisson sampling, which is the well-studied problem of drawing fixed-size subsets from a population with known inclusion probabilities. We give improved algorithms for carrying out this sampling, which may be of independent interest.

arXiv:2510.08518 [quant-ph]

(or arXiv:2510.08518v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.08518 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.