Related papers: Closed expressions for one-qubit states of convex roof coherence measures

Closed expressions for one-qubit states of convex roof coherence measures

URL: http://arxiv.org/abs/2308.03116v1
Date: Sun, 6 Aug 2023 13:51:46 GMT
Title: Closed expressions for one-qubit states of convex roof coherence measures
Authors: Xiao-Dan Cui and C. L. Liu
Abstract summary: We present the analytical expressions for the convex roof coherence measures for one-qubit states. Measures include the coherence of formation, the coherence measure coherence, the coherence rank.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study the closed expressions of the convex roof coherence measures for one-qubit states in this paper. We present the analytical expressions for the convex roof coherence measures, $C_f(\rho)$, of one-qubit states with $C_f(\varphi):=f(\abs{c_0}^2,\abs{c_1}^2)$ (where $\ket{\varphi}=c_0\ket{0}+c_1\ket{1}$) being convex with respect to the $l_1$ norm of coherence of $\varphi$ (i.e., $C_{l_1}(\varphi)$), such coherence measures including the coherence of formation, the geometric measure of coherence, the coherence concurrence, and the coherence rank. We further present the operational interpretations of these measures. Finally, we present the usefulness of the convex roof coherence measures $C_f(\varphi)$ being non-convex with respect to $C_{l_1}(\varphi)$ by giving the necessary and sufficient conditions for the transformations $p\varphi_1\oplus(1-p)\varphi_2\to q\phi_1\oplus(1-q)\phi_2$ via incoherent operations, where $\varphi_i$, $\phi_j$ $(i, j=1, 2)$ are one-qubit pure states and $0\leq p, q\leq 1$.

Related papers

Efficient Continual Finite-Sum Minimization [52.5238287567572]
We propose a key twist into the finite-sum minimization, dubbed as continual finite-sum minimization. Our approach significantly improves upon the $mathcalO(n/epsilon)$ FOs that $mathrmStochasticGradientDescent$ requires. We also prove that there is no natural first-order method with $mathcalOleft(n/epsilonalpharight)$ complexity gradient for $alpha 1/4$, establishing that the first-order complexity of our method is nearly tight.
arXiv Detail & Related papers (2024-06-07T08:26:31Z)
Synchronization on circles and spheres with nonlinear interactions [6.887244952811574]
We consider the dynamics of $n$ points on a sphere in $mathbbRd$ ($d geq 2$) which attract each other according to a function $varphi$ of their inner products. When $varphi$ is linear ($varphi(t) = t$, the points converge to a common value (i.e., synchronize) in various connectivity scenarios.
arXiv Detail & Related papers (2024-05-28T15:24:30Z)
Dimension Independent Disentanglers from Unentanglement and Applications [55.86191108738564]
We construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show that to capture NEXP, it suffices to have unentangled proofs of the form $| psi rangle = sqrta | sqrt1-a | psi_+ rangle where $| psi_+ rangle has non-negative amplitudes.
arXiv Detail & Related papers (2024-02-23T12:22:03Z)
On the $O(\frac{\sqrt{d}}{T^{1/4}})$ Convergence Rate of RMSProp and Its Momentum Extension Measured by $\ell_1$ Norm [59.65871549878937]
This paper considers the RMSProp and its momentum extension and establishes the convergence rate of $frac1Tsum_k=1T. Our convergence rate matches the lower bound with respect to all the coefficients except the dimension $d$. Our convergence rate can be considered to be analogous to the $frac1Tsum_k=1T.
arXiv Detail & Related papers (2024-02-01T07:21:32Z)
A Variational Quantum Algorithm For Approximating Convex Roofs [0.0]
entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. We produce a sequence of extensions that we call $f$-$d$ extensions, for $d in mathbbN$. We introduce a quantum variational algorithm which aims to approximate the $f$-$d$ extensions of entanglement measures defined on pure states.
arXiv Detail & Related papers (2022-03-04T02:30:35Z)
A first-order primal-dual method with adaptivity to local smoothness [64.62056765216386]
We consider the problem of finding a saddle point for the convex-concave objective $min_x max_y f(x) + langle Ax, yrangle - g*(y)$, where $f$ is a convex function with locally Lipschitz gradient and $g$ is convex and possibly non-smooth. We propose an adaptive version of the Condat-Vu algorithm, which alternates between primal gradient steps and dual steps.
arXiv Detail & Related papers (2021-10-28T14:19:30Z)
$l_{1}$ norm of coherence is not equal to its convex roof quantifier [0.6091702876917281]
We show that for the widely used coherence measure, $l_1$ norm of coherence $C_l_1$, it holds that $C_l_1neq overlineC_l_1$.
arXiv Detail & Related papers (2021-10-21T04:34:25Z)
Simplest non-additive measures of quantum resources [77.34726150561087]
We study measures that can be described by $cal E(rhootimes N) =E(e;N) ne Ne$.
arXiv Detail & Related papers (2021-06-23T20:27:04Z)
Linear Bandits on Uniformly Convex Sets [88.3673525964507]
Linear bandit algorithms yield $tildemathcalO(nsqrtT)$ pseudo-regret bounds on compact convex action sets. Two types of structural assumptions lead to better pseudo-regret bounds.
arXiv Detail & Related papers (2021-03-10T07:33:03Z)
Refining the general comparison theorem for Klein-Gordon equation [2.4366811507669124]
We recast the Klein-Gordon-Gordon equation as an eigen-equation in the coupling parameter $v > 0,$ the basic Klein-Gordon comparison theorem. We weaken the sufficient condition for the groundstate spectral ordering by proving. that if $intxbig[f_2(t)big]varphi_i(t)dtgeq 0$, the couplings remain ordered.
arXiv Detail & Related papers (2020-12-23T22:36:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.