A central task in quantum information science is state certification: testing whether an unknown state is ๐1-close to a fixed target state, or ๐2-far. Recent work has shown that surprisingly simple measurement protocolsโcomprising only single-qubit measurementsโsuffice to certify arbitrary ๐-qubit states [14, 18]. However, these certification protocols are not robust: rather than allowing constant ๐1, they can only positively certify states within ๐1 = ๐(1/๐) trace distance of the target. In many experimental settings, the appropriate error tolerance is constant as the system size grows, so this lack of robustness renders existing tests inapplicable at scale, no matter how many times the test is repeated. Here we present robust certification protocols based on few-qubit measurements that apply to all but a ๐(2โ๐)-fraction of pure targetstates. Our first protocol achieves constant robustness, i.e. ๐1 = ฮ(1),using a single ๐(log๐)-qubit measurement along with single-qubit measurements in the ๐ or ๐ basis on the other qubits. As a corollary of its robustness, this protocol also achieves constant (in ๐) copy complexity, which is optimal. Our second protocol uses exclusively single-qubit measurements and is nearly robust: ๐1 = ฮฉ(1/log๐). Our tests are based on a new uncertainty principle for conditional fidelities which may be of independent interest.
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Stabilizing two-qubit entanglement with dynamically decoupled active feedback
We propose and analyze a protocol for stabilizing a maximally entangled state of two noninteracting qubits using active state-dependent feedback from a continuous two-qubit half-parity measurement in coordination with a concurrent, noncommuting dynamical decoupling drive. We demonstrate that such a drive can be simultaneous with the measurement and feedback, while also playing a key part in the feedback protocol itself. We show that robust stabilization with near-unit fidelity can be achieved even in the presence of realistic nonidealities, such as time delay in the feedback loop, imperfect state-tracking, inefficient measurements, dephasing from 1/๐-distributed qubit-frequency noise, and relaxation. We mitigate feedback-delay error by introducing a forward-state-estimation strategy in the feedback controller that tracks the effects of control signals already in transit. More generally, the steady state is globally attractive without the need for ancillas, regardless of the error state, in contrast to most known feedback and error-correction schemes.
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- Award ID(s):
- 1936388
- PAR ID:
- 10565965
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Applied
- Volume:
- 21
- Issue:
- 2
- ISSN:
- 2331-7019
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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