Covariance Decomposition as a Universal Limit on Correlations in Networks

Universality of Schmidt decomposition and particle identity

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 paradigma…

Singlet state creation and Universal quantum computation in NMR using Genetic Algorithm

Experimental implementation of a quantum algorithm requires unitary operator decomposition. Here we treat the unitary operator decomposition as an optimization problem and use Genetic Algorithm, a global optimization method inspired by nature's evolutionary process for operator decomposition. As an application, we apply this to NMR Quantum Information Processing and find a probabilistic way of doing universal quantum computation using global hard pulses. We also demonstrate efficient creation of singlet state (as a special case of Bell state) directly from thermal equilibrium using an optimum …

Universal Prony fitting decomposition for optimized hierarchical quantum master equations

In this work, we propose the Prony fitting decomposition (PFD) as an accurate and efficient exponential series method, applicable to arbitrary interacting bath correlation functions. The resulting hierarchical equations of motion (HEOM) formalism is greatly optimized, especially in extremely low temperature regimes that would be inaccessible with other methods. For demonstration, we calibrate the present PFD against the celebrated Padé spectrum decomposition method, followed by converged HEOM evaluations on the single-impurity Anderson model system.

支持投影的Petz单调几何：纯双量子比特家族的通用三通道分解与曲率不变量非缩减

Support-Projected Petz Monotone Geometry of Pure Two-Qubit Families: Universal Three-Channel Decomposition and Non-Reduction of Curvature Invariants

本文提出了一种支持投影的Petz单调几何框架，用于纯双量子比特家族，实现了通用三通道分解并展示了曲率不变量的非缩减特性。

The Symplectic Camel and Quantum Universal Invariants: the Angel of Geometry vs. the Demon of Algebra

A positive definite symmetric matrix σ qualifies as a quantum mechanical covariance matrix if and only if σ+(1/2)i\hbarΩ\geq0 where Ω is the standard symplectic matrix. This well-known condition is a strong version of the uncertainty principle, which can be reinterpreted in terms of the topological notion of symplectic capacity, closely related to Gromov's non-squeezing theorem. We show that a recent refinement of the latter leads to a new class of geometric invariants. These are the volumes of the orthogonal projections of the covariance ellipsoid on symplectic subspaces of the phase space. W…

Parametric Number Covariance in Quantum Chaotic Spectra

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the co- variance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal non-invariant cases. A local version of the parametric number variance introduced earlier is also investigated.

量子场论通用性准则用于分层可编程分解

Quantum Field Theory Universality Criterion for Layered Programmable Decompositions

本文提出基于量子场论模型的通用性准则，用于验证分层可编程分解的通用性，通过分析混合矩阵集和参数化形式，证明其覆盖特殊酉群的条件，并提供确定性算法和几何优化方法。