A nonstabilizerness monotone from stabilizerness asymmetry

IF 5 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY
Poetri Sonya Tarabunga, Martina Frau, Tobias Haug, Emanuele Tirrito and Lorenzo Piroli
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Abstract

We introduce a nonstabilizerness monotone which we name basis-minimized stabilizerness asymmetry (BMSA). It is based on the notion of G-asymmetry, a measure of how much a certain state deviates from being symmetric with respect to a symmetry group G. For pure states, we show that the BMSA is a strong monotone for magic-state resource theory, while it can be extended to mixed states via the convex roof construction. We discuss its relation with other magic monotones, first showing that the BMSA coincides with the recently introduced basis-minimized measurement entropy, thereby establishing the strong monotonicity of the latter. Next, we provide inequalities between the BMSA and other nonstabilizerness measures such as the robustness of magic, stabilizer extent, stabilizer rank, stabilizer fidelity and stabilizer Rényi entropy. We also prove that the stabilizer fidelity, stabilizer Rényi entropy and BMSA with index have the same asymptotic scaling with qubit number. Finally, we present numerical methods to compute the BMSA, highlighting its advantages and drawbacks compared to other nonstabilizerness measures in the context of pure many-body quantum states. We also discuss the importance of additivity and strong monotonicity for measures of nonstabilizerness in many-body physics, motivating the search for additional computable nonstabilizerness monotones.
由稳定性不对称得到的非稳定性单调
我们引入了一个非稳定单调,我们称之为基最小化稳定不对称(BMSA)。它是基于g不对称的概念,一个衡量某一状态相对于对称群g偏离对称程度的度量。对于纯态,我们证明了BMSA是魔态资源理论的强单调,同时它可以通过凸顶结构扩展到混合态。我们讨论了它与其他神奇单调的关系,首先证明了BMSA与最近引入的基最小化测量熵重合,从而建立了后者的强单调性。其次,我们提供了BMSA与其他非稳定性度量(如magic的鲁棒性、稳定性程度、稳定性等级、稳定性保真度和稳定性r尼熵)之间的不等式。我们还证明了稳定器保真度、稳定器r熵和带指数的BMSA与量子位数具有相同的渐近标度。最后,我们提出了计算BMSA的数值方法,强调了它在纯多体量子态背景下与其他非稳定性度量相比的优点和缺点。我们还讨论了多体物理中可加性和强单调性对于非稳定测度的重要性,从而激发了对其他可计算非稳定测度的探索。
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来源期刊
Quantum Science and Technology
Quantum Science and Technology Materials Science-Materials Science (miscellaneous)
CiteScore
11.20
自引率
3.00%
发文量
133
期刊介绍: Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics. Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.
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