arXiv subjects

Fangmin Song

Publications and source records attributed to Fangmin Song.

6 recordsLinked to original sources

arXiv2021

Towards the standardization of quantum state verification using optimal strategies

Quantum devices for generating entangled states have been extensively studied and widely used. As so, it becomes necessary to verify that these devices truly work reliably and efficiently as they are specified. Here, we experimentally realize the recently proposed two-qubit entangled state verification strategies using both local measurements (nonadaptive) and active feed-forward operations (adaptive) with a photonic platform. About 3283/536 number of copies ($N$) are required to achieve a 99% confidence to verify the target quantum state for nonadaptive/adaptive strategies. These optimal strategies provide the Heisenberg scaling of the infidelity $ε$ as a function of $N$ ($ε$ $\sim$ $N^r$) with the parameter $r=-1$, exceeding the standard quantum limit with $r=-0.5$. We experimentally obtain the scaling parameter of $r=-0.88\pm$0.03 and $-0.78\pm$0.07 for nonadaptive and adaptive strategies, respectively. Our experimental work could serve as a standardized procedure for the verification of quantum states.

quant-ph↗

arXiv2018

Entanglement Detection via Direct-Sum Majorization Uncertainty Relations

In this paper we investigate the relationship between direct-sum majorization formulation of uncertainty relations and entanglement, for the case of two and many observables. Our primary results are entanglement detection methods based on direct-sum majorization uncertainty relations. These nonlinear detectors provide a set of necessary conditions for detecting entanglement whose number grows with the dimension of the state being detected.

quant-ph↗

arXiv2018

Uncertainty Relations in the Presence of Quantum Memory for Mutually Unbiased Measurements

In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased measurements. Our primary result is an equality between the amount of uncertainty for a set of measurements and the amount of entanglement of the measured state, both of which are quantified by the conditional collision entropy. Implications of this equality relation are discussed. We further show that similar equality relation can be obtained for generalized symmetric informationally complete measurements. We also derive an interesting equality for arbitrary orthogonal basis of the space of Hermitian, traceless operators.

quant-ph↗

arXiv2016

The Lackadaisical Quantum Walker is NOT Lazy at all

In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $τ$ self-loops. We derive an analytic expression for the localization probability of the walker at the origin after infinite steps, and obtain the peak velocities of the walker. We also calculate rigorously the wave function of the walker starting from the origin and obtain a long time approximation for the entire probability density function. As an application of the density function, we prove that lackadaisical quantum walks spread ballistically for arbitrary $τ$, and give an analytic solution for the variance of the walker's probability distribution.

quant-ph↗

arXiv2016

Grover Walks on a Line with Absorbing Boundaries

In this paper, we study Grover walks on a line with one and two absorbing boundaries. In particular, we present some results for the absorbing probabilities both in a semi-finite and finite line. Analytical expressions for these absorbing probabilities are presented by using the combinatorial approach. These results are perfectly matched with numerical simulations. We show that the behavior of Grover walks on a line with absorbing boundaries is strikingly different from that of classical walks and that of Hadamard walks.

quant-ph↗

arXiv2011

On Measurement and Computation

Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various physical mechanisms is discussed. Here, we focus on using it to review the theory of Quantum Computation. As a preliminary study on more general problems, some examples of other physical mechanism are also given in this paper.

physics.comp-ph↗