Abstract
The manipulation of quantum “resources” such as entanglement, coherence, and magic states lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to “purify” the quantum resources since they are inevitably contaminated by noise and thus often lose their power or become unreliable for direct usage. Here we prove fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource. More explicitly, we derive nontrivial lower bounds on the error of converting any full-rank noisy state to any target pure resource state by any free protocol (including probabilistic ones)—it is impossible to achieve perfect resource purification, even probabilistically. Our theorems indicate strong limits on the efficiency of distillation, a widely used type of resource purification routine that underpins many key applications of quantum information science. In particular, this general result induces the first explicit lower bounds on the resource cost of magic state distillation, a leading scheme for realizing scalable fault-tolerant quantum computation. Implications for the standard error-correction-based methods are specifically discussed.
- Received 17 September 2019
- Revised 26 February 2020
- Accepted 30 June 2020
DOI:https://doi.org/10.1103/PhysRevLett.125.060405
© 2020 American Physical Society
Physics Subject Headings (PhySH)
synopsis
Limits on Purifying Quantum States
Published 6 August 2020
A new theoretical study identifies fundamental tradeoffs that limit the amount of noise reduction in quantum information systems.
See more in Physics