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Kan He

Publications and source records attributed to Kan He.

30 records · Page 2Linked to original sources
arXiv2024

A norm inequality on noncommutative symmetric spaces related to a question of Bourin

In this note, we study a question introduced by Bourin \cite{2009Matrix} and partially solve the question of Bourin. In fact, for t\in[0,\frac{1}{4}]\cup[\frac{3}{4},1], we show that |||x^{t}y^{1-t}+y^{t}x^{1-t}|||\leq|||x+y|||, where x,y\in\mathbb{M}_{n}(\mathbb{C})^+ and \||\cdot\|| is the unitarily invariant norm. Moreover, we prove that the above inequality holds on noncommutative fully symmetric spaces.

math.FA↗
arXiv2023

Star network non-n-local correlations can resist consistency noises better

Imperfections from devices can result in the decay or even vanish of non-n-local correlations as the number of parties n increases in the polygon and linear quantum networks ([Phys. Rev. A 106, 042206 (2022)] and [Phys. Rev. A 107, 032404 (2023)]). Even so this phenomenon is also for the special kind of noises, including consistency noises of a sequence of devices, which means the sequence of devices have the same probability fails to detect. However, in the paper, we discover that star network quantum non-n-local correlations can resist better consistency noises than these in polygon and linear networks. We first calculate the noisy expected value o f star network non-n-locality and analyze the persistency conditions theoretically. When assume that congener devices have the consistency noise, the persistency number of sources n has been rid of such noises, and approximates to the infinity. Polygon and linear network non-n-local correlations can not meet the requirements. Furthermore, we explore the change pattern of the maximal number of sources nmax such that non-nmax-local correlation can be demonstrated in the star network under the influence of partially consistent noises, which is more general than consistent ones.

quant-ph↗
arXiv2022

Violating the bilocal inequality with separable mixed states in the entanglement-swapping network

It has been showed that two entangle pure states can violate the bilocal inequality in the entanglement-swapping network, vice versa. What happens for mixed states? Whether or not are there separable mixed states violating the bilocal inequality? In the work, we devote to finding the mixed Werner states which violate the bilocal inequality by Particle Swarm Optimization (PSO) algorithms. Finally, we shows that there are pairs of states, where one is separable and the other is entangled, can violate the bilocal inequality.

quant-ph↗
arXiv2022

Approximate separation of quantum gates and separation experiments of CNOT based on Particle Swarm Optimization algorithm

Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. It has been showed that there are few separable multipartite quantum gates, so the approximate separation problem involves finding local quantum gates that approximate a given inseparable gate. We propose and study a problem involving the approximate separation of multipartite gates based on quantum-gate fidelity. For given multipartite and local gates, we conclude that the smaller is the maximal distance between the products of an arbitrary pair of eigenvalues, the greater is their gate fidelity. This provides a criterion for approximate separation. Lastly, we discuss the optimal approximate separation of the CNOT gate.

quant-ph↗
arXiv2021

Separation of gates in quantum parallel programming

The number of qubits in current quantum computers is a major restriction on their wider application. To address this issue, Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. In this study, we theoretically analyse the (sufficient and necessary) separability conditions of multipartite quantum gates in finite or infinite dimensional systems. We then conduct separation experiments with n-qubit quantum gates on IBM quantum computers using QSI software.

quant-ph↗
arXiv2021

Detected the steerability bounds of the generalized Werner states via BackPropagation neural network

We use error BackPropagation (BP) neural network to determine whether an arbitrary two-qubit quantum state is steerable and optimize the steerability bounds of the generalized Werner state. The results show that no matter how we choose the features for the quantum states, we can use the BP neural network to construct several models to realize high-performance quantum steering classifiers compared with the support vector machine (SVM). In addition, we predict the steerability bounds of the generalized Werner states by using the classifiers which are newly constructed by the BP neural network, that is, the predicted steerability bounds are closer to the theoretical bounds. In particular, high-performance classifiers with partial information of the quantum states which we only need to measure in three fixed measurement directions are obtained.

quant-ph↗
arXiv2021

Quantifying measurement-induced nonbilocal correlation

In the paper, we devote to defining an available measure to quantify the nonbilocal correlation in the entanglement-swapping experiment. Then we obtain analytical formulas to calculate the quantifier when the inputs are pure states. For the case of mixed inputs, we discuss the computational properties of the quantifier. Finally, we derive a tight upper bound to the nonbilocality quantifier.

quant-ph↗
arXiv2018

Characterizing the Gaussian coherence-breaking channel and its property with assistant entanglement inputs

In the paper, we give a characterization of arbitrary $n$-mode Gaussian coherence breaking channels (GCBCs) and show the tensor product of a GCBC and arbitrary a Gaussian channel maps all input states into product states. The inclusion relation among GCBCs, Gaussian positive partial transpose channels (GPPTC), entanglement breaking channels (GEBC) and Gaussian classical-quantum channels (GCQC) is displayed. Finally, we prove that Gaussian classical ($χ$-) capacity for the tensor products of GCBCs and arbitrary Gaussian channels is additive.

quant-ph↗
arXiv2016

Uncertainty relations for any multi observables

Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal uncertainty relation for any $k$ observables, of which the formulation depends on the even or odd quality of $k$. This universal uncertainty relation is tight at least for the cases $k=2n$ and $k=3$. For two observables, the uncertainty relation is exactly a simpler reformulation of Schrödinger's uncertainty principle.

quant-ph↗
arXiv2012

A geometric characterization of invertible quantum measurement maps

A geometric characterization is given for invertible quantum measurement maps. Denote by ${\mathcal S}(H)$ the convex set of all states (i.e., trace-1 positive operators) on Hilbert space $H$ with dim$H\leq \infty$, and $[ρ_1, ρ_2]$ the line segment joining two elements $ρ_1, ρ_2$ in ${\mathcal S}(H)$. It is shown that a bijective map $ϕ:{\mathcal S}(H) \rightarrow {\mathcal S}(H)$ satisfies $ϕ([ρ_1, ρ_2]) \subseteq [ϕ(ρ_1),ϕ(ρ_2)]$ for any $ρ_1, ρ_2 \in {\mathcal S}$ if and only if $ϕ$ has one of the following forms $$ρ\mapsto \frac{MρM^*}{{\rm tr}(MρM^*)}\quad \hbox{or} \quad ρ\mapsto \frac{Mρ^T M^*}{{\rm tr}(Mρ^T M^*)},$$ where $M$ is an invertible bounded linear operator and $ρ^T$ is the transpose of $ρ$ with respect to an arbitrarily fixed orthonormal basis.

quant-ph↗