Kirkwood-Dirac Nonpositivity is a Necessary Resource for Quantum Computing
Univ. of Cambridge（剑桥大学）；Hitachi Cambridge Lab.（日立剑桥实验室）；Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（美国国家标准与技术研究院与马里兰大学量子信息与计算科学联合中心）；Institute for Physical Science and Technology, University of Maryland（马里兰大学物理科学与技术研究所）；Univ. Lille, CNRS, Inria, UMR 8524, Laboratoire Paul Painlevé（里尔大学、法国国家科学研究中心、法国研究计算机科学与应用数学研究所，保罗·潘勒瓦实验室（UMR 8524））
Jonathan J. Thio, Songqinghao Yang, Nicole Yunger Halpern, Stephan De Bièvre, Crispin H. W. Barnes, David R. M. Arvidsson-Shukur
We elucidate the boundary between classical and quantum computation by constructing qubit Clifford circuits with nonstabilizer inputs that can be efficiently simulated classically. We do so by casting the quantum circuits realizable by defect braiding in the surface code in terms of a Kirkwood-Dirac (KD) quasiprobability distribution, a generalization of a joint probability distribution. If this distribution remains a proper (positive) probability distribution throughout a circuit, then a classical algorithm can simulate the circuit efficiently. By leveraging recent results on the geometry of KD-positive states, we construct bound-magic states. Classical computers can efficiently simulate these bound-magic states' evolutions under the circuits, although other magic states enable universal quantum computation when inputted. Furthermore, we show that KD nonpositivity is a resource monotone in this model. Thus, we establish KD nonpositivity as a necessary resource for quantum-computational advantages.
Bounding Kirkwood-Dirac negativity of Gaussian processes
University of Florence（佛罗伦萨大学）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所（CNR-INO））；Università di Bologna and INFN, Sezione di Bologna（博洛尼亚大学和意大利国家核物理研究所博洛尼分所）；Paderborn University（帕德博恩大学）
Given two orthonormal bases in a d-dimensional Hilbert space, one associates to each state its Kirkwood-Dirac (KD) quasi-probability distribution. KD-nonclassical states - for which the KD-distribution takes on negative and/or nonreal values - have been shown to provide a quantum advantage in quantum metrology and information, raising the question of their identification. Under suitable conditions of incompatibility between the two bases, we provide sharp lower bounds on the support uncertainty of states that guarantee their KD-nonclassicality. In particular, when the bases are completely inco…
Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, our aim is two-fold: First, we highlight the role played by quasiprobabilities in characterizing the statistics of quantum observables and …
Kirkwood-Dirac classical states based on discrete Fourier transform: Representation with directed graph
School of Mathematics, South China University of Technology（华南理工大学数学学院）；School of Mathematics and Information Science, Henan Polytechnic University（河南理工大学数学与信息科学学院）
Temporal Kirkwood-Dirac Quasiprobability Distribution and Unification of Temporal State Formalisms through Temporal Bloch Tomography
Institute of Quantum Physics, School of Physics, Central South University（中南大学物理学院量子物理研究所）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Science, Mathematics and Technology Cluster, Singapore University of Technology and Design（新加坡科技设计大学科学、数学与技术集群）
What is special about the Kirkwood-Dirac distributions? Only they produce natural conditional expectations
Univ. Lille, CNRS, Inria, UMR 8524, Laboratoire Paul Painlevé（里尔大学）；Univ. Reims Champagne-Ardenne, CNRS, UMR 9008, Laboratoire Mathématique de Reims（兰斯香槟-阿登大学）
Almost no experiments have classical Kirkwood-Dirac representations
Univ. Lille, CNRS, Inria, UMR 8524, Laboratoire Paul Painlevé（里尔大学）；Hitachi Cambridge Lab.（日立剑桥实验室）；DAMTP, Centre for Mathematical Sciences, Univ. of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）；Cavendish Lab., Department of Physics, Univ. of Cambridge（剑桥大学卡文迪许实验室）
Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood-Dirac (KD) distribution has been employed to study nonclassicality across quantum physics, from metrology to chaos to the foundations of quantum theory. The KD distribution is a quasiprobability distribution, a quantum generalization of a probability distribution, which can behave nonclassically by having negative or nonreal elements. Negative KD elements signify quantum information scrambling and potential metrological quantum advantages. Nonrea…
Revealing the topology of quantum states via Kirkwood-Dirac quasiprobabilities
Istituto Nazionale di Ottica (INO), Consiglio Nazionale delle Ricerche（意大利国家光学研究所，意大利国家研究委员会）；European Laboratory for Non-linear Spectroscopy (LENS), Università di Firenze（欧洲非线性光谱学实验室，佛罗伦萨大学）；Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma（帕尔马大学数学、物理与信息科学系）；Gruppo Collegato di Parma, INFN-Sezione Milano-Bicocca（帕尔马联合小组，INFN米兰比可卡分部）；UdR Parma, INSTM（帕尔马研究组，意大利材料科学与技术研究中心）
Nonclassical energy-change distribution as a witness of non-Markovian quantum dynamics
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；Centro de Física e Engenharia de Materiais Avançados (CeFEMA), Laboratory of Physics for Materials and Emerging Technologies (LaPMET), and PQI – Portuguese Quantum Institute, Portugal（葡萄牙高级材料与工程物理中心、材料与技术新兴物理实验室及葡萄牙量子研究所）；Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain（巴塞罗那自治大学物理系理论物理：信息与量子现象部门）；Università degli Studi di Palermo, Dipartimento di Fisica e Chimica – Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy（巴勒莫大学埃米利奥·塞格雷物理化学系）；European Laboratory for Non-linear Spectroscopy, Università di Firenze, I-50019 Sesto Fiorentino, Italy（佛罗伦萨大学欧洲非线性光谱学实验室）
Theory of direct measurement of the quantum pseudo-distribution via its characteristic function
Institute for Quantum Studies, Chapman University（查普曼大学量子研究所）；Department of Physics and Astronomy, University of Rochester（罗切斯特大学物理与天文学系）；Hitachi Cambridge Laboratory（日立剑桥实验室）；Department of Physics, University of Toronto（多伦多大学物理系）
Quantum work statistics and coherence effects in quenched bosonic Josephson junctions
Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；European Laboratory for Non-linear Spectroscopy, Università di Firenze（佛罗伦萨大学欧洲非线性光谱学实验室）；Department of Physics and Astronomy, University of Florence（佛罗伦萨大学物理与天文学系）
