Physical Implementability of Linear Maps and Its Application in Error Mitigation

• DOI: 10.22331/q-2021-12-07-600
• Publication Date: 2021-12-07T14:05:17Z
• Authors: Jiaqing Jiang; Kun Wang; Xin Wang
• Keywords: TRACE (psycholinguistics)

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as but not completely which can be implemented, are fundamental ingredients in information, both theoretical practical perspectives. This raises question of how well one simulate or approximate action a map by In this work, we introduce systematic framework to resolve task using quasiprobability decomposition technique. We decompose target into combination operations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">physical implementability</mml:mtext></mml:mrow></mml:math> measure least amount negative portion that must pertain, directly quantifies cost simulating given show is efficiently computable semidefinite programs prove several properties measure, faithfulness, additivity, unitary invariance. derive lower upper bounds terms Choi operator's trace norm obtain analytic expressions for interests. Furthermore, endow with an operational meaning within error mitigation scenario: it establishes bound sampling achievable via particular, parallel noises, global has no advantage over local mitigation.