Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to exist for identical particles, an open problem forbidding its application to analyze such many-body quantum systems. Here we prove, using a newly developed approach, that the Schmidt decomposition exists for identical particles and is thus universal. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in separated places. For the case of two qutrits in the same place, we show that their entanglement behavior, whose physical interpretation is given, differs from that obtained before by different methods. Our results are generalizable to multiparticle systems and open the way for further developments in quantum information theory when particle identity counts as a resource.
In this report we are aiming at introducing a global measure of non-classicality of the state space of $N$-level quantum systems and estimating it in the limit of large $N$. For this purpose we employ the Wigner function negativity as a non-classicality criteria. Thus, the specific volume of the support of negative values of Wigner function is treated as a measure of non-classicality of an individual state. Assuming that the states of an $N$-level quantum system are distributed by Hilbert-Schmidt measure (Hilbert-Schmidt ensemble), we define the global measure as the average non-classicality o…
Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. Given a pure state of the system and a division into regions $A$ and $B$, they can be obtained in terms of the $Schmidt~ values$, or eigenvalues $λ_α$ of the reduced density matrix $ρ_A$ for region $A$. In this paper we draw attention instead to the $Schmidt~ vectors$, or eigenvectors $|v_α\rangle$ of $ρ_A$. We consider the ground state of critical quantum spin chains whose low energy/long distance physics is described by an emergent conformal field theory (C…
Local Universality and Structural Certificates for Minimal Fixed-Depth Two-Qutrit Gate Decomposition
National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理学院、先进微结构协同创新中心）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息与量子科技重点实验室）；Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications（南京邮电大学量子信息技术研究所）；State Key Laboratory of Quantum Optics and Devices, Shanxi University（山西大学量子光学与器件国家重点实验室）
Local universality of non-local quantum resources in rotationally invariant scattering
InQubator for Quantum Simulation (IQuS) and Department of Physics, University of Washington（华盛顿大学量子模拟创新中心及物理系）；Institute for Quantum Information and Matter (IQIM) and Department of Physics, California Institute of Technology（加州理工学院量子信息与物质研究所及物理系）
Universal and non-universal facets of quantum critical phenomena unveiled along the Schmidt decomposition theorem
São Paulo State University (Unesp)（圣保罗州立大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Santa Fe Institute（圣塔菲研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）
Universality from Quadratic Angular-Momentum Operations: Exact Dynamical Lie Algebras and the Role of the Casimir Obstruction
Forschungszentrum Jülich（于利希研究中心）；Universität des Saarlandes（萨尔兰大学）；Université Paris Cité, CNRS, Laboratoire Matériaux et Phénomènes Quantiques（巴黎西岱大学，法国国家科学研究中心，材料与量子现象实验室）
Universal entanglement detection with geometrically optimal witnesses
Southern University of Science and Technology（南方科技大学）；The Hong Kong University of Science and Technology（香港科技大学）；Quantum Science Center of Guangdong-HongKong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；The University of Hong Kong（香港大学）
