Highly-entangled, highly-doped states that are efficiently cross-device verifiable

TL;DR

This paper introduces a class of highly entangled, highly-doped quantum states that are efficiently verifiable across devices using Bell sampling, even when classical descriptions are insufficient, with scalable and robust methods suitable for near-term implementation.

Contribution

It demonstrates that cross-device verification of complex quantum states is possible without classical descriptions, using scalable Bell sampling techniques.

Findings

Efficient cross-device verification for complex quantum states.

Verification method scalable with qubits and error tolerance.

Robust against preparation errors and implementable in near-term experiments.

Abstract

In this paper, we introduce a class of highly entangled real quantum states that cannot be approximated by circuits with $\log$-many non-Clifford gates and prove that Bell sampling enables efficient cross-device verification (or distributed inner product estimation) for these states. That is, two remote parties can estimate the inner product ${\rm tr}(\rho\sigma)$, each having black-box access to copies of a state $\rho$ (or respectively $\sigma$) in this class. This is significant because it is clear that this task can be achieved in those cases (such as low entanglement or low non-Clifford gate count) where one can independently learn efficient classical descriptions of each state using established techniques and share the description to compute the overlap. Instead, our results demonstrate that this is possible even in more complex scenarios where these "learn and share" methods are insufficient. Our proposal is scalable, as it just requires a number of two-copy Bell measurements and single-copy Pauli measurements that grows polynomially with both the number of qubits and the desired inverse-error, and can be implemented in the near term. Moreover, the required number of samples can be efficiently experimentally determined by the parties in advance, and our findings are robust against preparation errors. We anticipate that these results could have applications in quantum cryptography and verification.