We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are proposed, in particular concerning Gaussian wave-packet propagation under classically regular dynamics.
An Algorithm for Estimating $α$-Stabilizer Rényi Entropies via Purity
Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol（量子工程博士培训中心，H.H.威尔斯物理实验室和电气与电子工程系，布里斯托大学）；H.H. Wills Physics Laboratory, University of Bristol（H.H.威尔斯物理实验室，布里斯托大学）
Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work we show that they can also be used to establish semi-device independent lower bounds on the purity of the initial quantum state or even on one of the post-measurement states. For single systems this provides information on the quality of the preparation procedures of pure states or the implementation of measurements with anticipated pure post-measurement states. For joint systems one can combine our bound with results fro…
Various quantum technology applications require high-purity single photons with high generation rate. Although different methods are employed to generate such photons, heralded single photons from spontaneous parametric down-conversion (SPDC) is the most commonly used approach. Photon generation rate from the heralded single-photon sources are limited by the efficiency of the detectors to record coincidence detection of the photon pairs which are lower than the single-photon counts recorded separately on each detector. In this paper we present a revised expression to calculate second-order tem…
Different degrees of freedom of single photons have been entangled and are used as a resource for various quantum technology applications. We present a simple scheme to perform Bell's test and show the violation of CHSH inequality in a path-entangled single photon state using interferometric and its equivalent non-interferometric approach in beam splitter setting. We demonstrate this experimentally by generating and controlling path-entangled state using both, heralded and un-heralded single photons from spontaneous parametric down-conversion. The experimental results we present show the trans…
Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology（国际信息技术学院计算自然科学与生物信息中心）；International Institute of Information Technology, Hyderabad（海得拉巴国际信息技术学院）；Center for Quantum Science and Technology, International Institute of Information Technology（国际信息技术学院量子科学与技术中心）
The quantum phase diagram for a finite $3$-level system in the $Λ$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility and entanglement, applied to the reduced density matrix of the matter sector of the system. The quantum phases are explained by emphasizing the spontaneous symmetry breaking along the separatrix. Additionally, a description of the reduced density matrix of one atom in terms of a simplex allows a geometric representation of the entanglement and purity properties of…
The Wigner function's behavior of accelerated and non-accelerated Greenberger Horne Zeilinger (GHZ) state is discussed. For the non-accelerated GHZ state, the minimum/maximum peaks of the Wigner function depends on the distribution's angles, where they are displayed regularly at fixed values of the distribution's angles. We show that, for the accelerated GHZ state, the minimum bounds increases as the acceleration increases. The increasing rate depends on the number of accelerated qubits. Due to the positivity/ negativity behavior of the Wigner function, one can use it as an indicators of the p…
Quantum teleportation and dynamics of quantum coherence and metrological non-classical correlations for open two-qubit systems: A study of Markovian and non-Markovian regimes
Machine learning has achieved success in many areas because of its powerful fitting ability, so we hope it can help us to solve some significant physical quantitative problems, such as quantum correlation. In this research we will use neural networks to predict the value of quantum discord. Quantum discord is a measure of quantum correlation which is defined as the difference between quantum mutual information and classical correlation for a bipartite system. Since the definition contains an optimization term, it makes analytically solving hard. For some special cases and small systems, such a…
Estimating the quality of a single-photon source is crucial for its use in quantum technologies. The standard test for semiconductor sources is a value of the second-order correlation function of the emitted field below $1/2$ at zero time-delay. This criterion alone provides no information regarding the amplitude of the single-photon contribution for general quantum states. Addressing this question requires the knowledge of additional observables. We derive an effective second-order correlation function, strongly connected to the Mandel-$Q$ parameter and given in terms of both the second-order…
We present marginal cumulative distribution functions (CDF) for density matrices $ρ$ of fixed purity $\tfrac{1}{N}\leμ_N(ρ)=\textrm{Tr}[ρ^2]\le 1$ for arbitrary dimension $N$. We give closed form analytic formulas for the cases $N=2$ (trivial), $N=3$ and $N=4$, and present a prescription for CDFs of higher arbitrary dimensions. These formulas allows one to uniformly sample density matrices at a user selected, fixed constant purity, and also detail how these density matrices are distributed nonlinearly in the range $μ_N(ρ)\in[\tfrac{1}{N}, 1]$. As an illustration of these formulas, we compare t…
