Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by the non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWF) allow a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of such single-particle pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light-matter interaction phenomena in a resonant tunneling device (RTD), where a single photon is interacting with a single electron. Third, we emphasize the importance of interpreting such scattering mechanism as a transition between initial and final single-particle BCWF with well-defined energies (rather than with well-defined momenta).
Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows one to straightforwardly define a quantum motion, a Bohmian mechanics, on shape space. We show how this motion gives rise to the more or less familiar theory in absolute space and time. We find that free motion on shape space, when lifted to configuration space, becomes an interacting theory. Many different lifts are possible corresponding in fact to differ…
Modified logarithmic Sobolev inequality for 1D non-commuting Hamiltonians
University of Cambridge（剑桥大学）；Universität Tübingen（蒂宾根大学）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Instituto de Ciencias Matemáticas (ICMAT)（数学科学研究所）；Instituto de Física Teórica UAM/CSIC（UAM/CSIC理论物理研究所）
A prominent tool to study the dynamics of open quantum systems is the reduced density matrix. Yet, approaching open quantum systems by means of state vectors has well known computational advantages. In this respect, the physical meaning of the so-called conditional states in Markovian and non-Markovian scenarios has been a topic of recent debate in the construction of stochastic Schrödinger equations. We shed light on this discussion by acknowledging the Bohmian conditional wavefunction as the proper mathematical object to represent, in terms of state vectors, an arbitrary subset of degrees of…
Many applications of practical interest rely on time evolution of Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to sums of commuting Paulis by concatenating the circuits of individual terms. In this paper we reduce the circuit complexity of Hamiltonian simulation by partitioning the Pauli operators into mutually commuting clusters and exponentiating the elements within each cluster after applying simultaneous diagonalization. We provide a practical algorithm for partitio…
Bipartite separability of one parameter families of states using conditional quantum relative Tsallis entropy
Kuvempu University（库韦姆普大学）；Inspire Institute Inc.（Inspire研究所）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Institute of Mathematical Sciences（数学科学研究所）；Bangalore University（班加罗尔大学）
Computation of many-particle quantum trajectories with exchange interaction: Application to the simulation of nanoelectronic devices
根据参考文献[Oriols X 2007 Phys.Rev.Lett.，98 066803]，提出了一种处理不可分量子系统中交换相互作用的算法.该算法可以应用于费米子或玻色子，通过构造，它可以确保任何可观察粒子完全独立于粒子的交换。它是基于使用的条件波函数，这是解决方案的单粒子伪薛定谔方程。交换对称性直接通过要求量子轨道在位形空间中的对称性来定义，而不是通过在单粒子赝薛定谔方程中引入特定的交换关联泛函来定义.它需要计算N^2个条件波函数来处理N个相同的粒子。对于可分的哈密顿量，算法简化为费米子的标准斯莱特行列式，或玻色子的永久行列式。一个两粒子系统的数值测试，其中的精确解的不可分的哈密顿计算访问，提出。量子电子输运（在一个远离平衡的时间依赖性开放系统）的算法的数值可行性证明通过计算纳米电阻器中的电流和波动，与交换和库仑电子之间的相互作用。
Quantum steering is equivalent to state-preserving conditional expectations
Perimeter Institute for Theoretical Physics（佩里尔理论物理研究所）；Institute for Quantum Computing（量子计算研究所）；Unité de Mathématiques Pures et Appliquées, CNRS - ENS Lyon（纯粹与应用数学单位，法国国家科学研究中心-里昂高等师范学院）；Leibniz Universität Hannover, Institut für Theoretische Physik（汉诺威莱布尼茨大学理论物理研究所）
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）
Hardware-Agnostic Modeling of Quantum Side-Channel Leakage via Conditional Dynamics and Learning from Full Correlation Data
Know Center GmbH（Know Center有限公司）；University of Graz（格拉茨大学）；Stevens Institute of Technology（史蒂文斯理工学院）；Technische Universität Wien（维也纳工业大学）；IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
Fachbereich Mathematik, Universität Tübingen（蒂宾根大学数学系）；Dep. of App. Mathematics and Theo. Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris（巴黎理工学院电信学院LTCI实验室法国国家信息与自动化研究所）
Institute for Advancing Intelligence, TCG CREST（TCG CREST 推进智能研究所）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算科学联合中心）
