Using Stein's estimator to correct the bound on the entropic uncertainty principle for more than two measurements

Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements

Information-theoretic definitions for noise and disturbance in quantum measurements were given in Phys. Rev. Lett. 112, 050401 (2014) and a state-independent noise-disturbance uncertainty relation was obtained. Here, we derive a tight noise-disturbance uncertainty relation for complementary qubit observables and carry out an experimental test. Successive projective measurements on the neutron's spin-1/2system, together with a correction procedure which reduces the disturbance, are performed. Our experimental results saturate the tight noise-disturbance uncertainty relation for qubits when an o…

通过快速Stein校正利用量子退火机进行Boltzmann采样

Boltzmann sampling with quantum annealers via fast Stein correction

本文提出一种基于随机特征映射和指数梯度更新的快速近似方法，用于量子退火机生成样本的Stein校正，显著降低热平均计算的残差误差，为量子退火替代传统MCMC方法提供可能。

On entropic uncertainty relations in the presence of a minimal length

Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum operators satisfy the modified commutation relation, for which more than one algebraic representation is known. One of them is described by auxiliary momentum so that the momentum and coordinate wave functions are connected by the Fourier transform. However, the probability density functions of the physically true and auxiliary momenta are different. As the …

Entropic uncertainty relations for successive measurements in the presence of a minimal length

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. Here, specific features of measurements of observables with continuous spectra should be taken into account. First, we formulated uncertainty relations in terms of Shannon entropies. Since such relations involve a state-dependent correction term, they generally differ from preparation uncertainty relations. This difference is revealed when position is measured by the first. In contrast, state-independent…

$κ$-熵统计范式用于海森堡原理的相对论修正

$κ$-entropic statistical paradigm for relativistic corrections to the Heisenberg principle

本文基于$κ$-变形Kaniadakis统计，推导了相对论扩展的海森堡代数，探讨了相对论修正的不确定性关系及其物理影响。

Entropic proofs of Singleton bounds for quantum error-correcting codes

We show that a relatively simple reasoning using von Neumann entropy inequalities yields a robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC). For entanglement-assisted quantum error-correcting codes (EAQECC) and catalytic codes (CQECC), a type of generalized quantum Singleton bound [Brun et al., IEEE Trans. Inf. Theory 60(6):3073--3089 (2014)] was believed to hold for many years until recently one of us found a counterexample [MG, Phys. Rev. A 103, 020601 (2021)]. Here, we rectify this state of affairs by proving the correct generalized quantum Singleton bou…