Relaxed uncertainty relations and information processing

Lower bound of local quantum uncertainty for high-dimensional bipartite quantum systems

Quantum correlations are of fundamental importance in quantum phenomena and quantum information processing studies. The measure of quantum correlations is one central issue. The recently proposed measure of quantum correlations, the local quantum uncertainty (LQU), satisfies the full physical requirements of a measure of quantum correlations. In this work, by using operator relaxation, a closed form lower bound of the LQU for arbitrary-dimensional bipartite quantum states is derived. We have compared the lower bound and the optimized LQU for several typical quantum states.

The Physics of Quantum Information: Complementarity, Uncertainty, and Entanglement

The overarching goal of this thesis is to demonstrate that complementarity is at the heart of quantum information theory, that it allows us to make (some) sense of just what information "quantum information" refers to, and that it is useful in understanding and constructing quantum information processing protocols. The detailed research results which form the basis of these claims are to be found in the included papers, and the aim here is to present an overview comprehensible to a more general audience.

A note on uncertainty relations of metric-adjusted skew information

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fi…

The complementarity relations of quantum coherence in quantum information processing

We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertaintylike expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.

Uncertainty Relation for the Discrete Fourier Transform

We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two mutually unbiased bases related by a Discrete Fourier Transform. It provides an uncertainty relation which smoothly interpolates between the well known cases of the Pauli operators in 2 dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal process…

Relative entropy derivation of the uncertainty principle with quantum side information

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle can be viewed as a data-processing inequality, a special case of the notion that information cannot increase due to evolution in time. This leads to a systematic method for finding the minimum uncertainty states of various entropic uncertainty relations; interestingly such states are intimately connected with the reversibility of time evolution.

统一不确定性量化框架：跨越变分量子算法和量子信号处理中的噪声量子后端

Unified Uncertainty Quantification Framework Bridging Noisy Quantum Backends Across Variational Quantum Algorithms and Quantum Signal Processing

该研究提出统一不确定性量化框架，在同一统计管道下比较NISQ变分量子算法和基于QSVT的格林函数重建两类工作负载，结合多种分析方法，能识别相关特性，为不同工作负载提供通用基准来衡量后端可靠性。

Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels

We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy. As a special case, it gives an improved data processing inequality.

量子引力模拟：基于广义不确定性原理的最小长度量子模拟

Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle

该研究提出用\(L\)个量子比特模拟一维量子系统的方法，推导广义不确定性原理，探讨其在低能和高能情况的性质，给出高能动量新表达式及相关特定情况分析，为用量子模拟研究高能量子引力现象提供新途径。