Lin Zhang, Junde Wu, Shao-Ming Fei
In this paper, we characterize the saturation of four universal inequalities in quantum information theory, including a variant version of strong subadditivity inequality for von Neumann entropy, the coherent information inequality, the Holevo quantity and average entropy inequalities. These results shed new light on quantum information inequalities.
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The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a regularizer for low-rank matrix recovery. The norm constants that bound the diamond norm in terms of the nuclear norm (also known as trace norm) are explicitly known. This note provides a simple characterization of all operators saturating the upper and the lower bound.
Efficiently bounding large determinants is an essential step in non-relativistic fermionic constructive quantum field theory to prove the absolute convergence of the perturbation expansion of correlation functions in terms of powers of the strength $u\in \mathbb{R}$ of the interparticle interaction. We provide, for large determinants of fermionic convariances, sharp bounds which hold for all (bounded and unbounded, the latter not being limited to semibounded) one-particle Hamiltonians. We find the smallest universal determinant bound to be exactly $1$. In particular, the convergence of perturb…
Entropy Inequalities Constrain Holographic Erasure Correction
该研究从擦除纠错视角解释全息熵不等式，指出某不等式不饱和是特定全息擦除纠错方案的必要条件，且在体中体现为对应纠缠楔非空重叠。
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki $L_p$ spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from (Sutter, Berta \& Tomamichel 2017). Then, using the Haag…
Universality of state-independent violation of correlation inequalities for noncontextual theories
我们表明，状态独立违反非上下文隐变量理论中引入的不等式[物理。101，210401（2008）]是普遍的，即，任何量子力学系统都有可能发生这种情况，在这种系统中，非上下文是有意义的。我们描述了一种方法来获得状态独立的侵犯任何系统的尺寸d > 2。这种普适性证明，根据量子力学，不存在“经典”态。
New entropic inequalities are obtained for Franck-Condon factors (FCF-s) of diatomic molecules in adiabatic harmonic oscillator approximation. The probability distributions associated with FCF-s of diatomic molecules are presented in the form of joint-probability distributions of either two or three random variables. In view of this representation information inequalities corresponding to subadditivity condition is found and in case of harmonic oscillator approximation is obtained in explicit form of new inequalities for Hermite polynomials. Physical meaning of obtained entropic-information in…
Universal violation of pentagon inequalities in four-state systems
从600个单元格的顶点导出的60个实向量产生了一些五边形不等式，这些不等式满足现实的非上下文理论，但违反了量子力学。这些不等式的复制品如此密集地覆盖希尔伯特空间，以至于每个实四维向量都至少违反其中之一。有人指出，这一组60个向量包含许多“N-角”（概括的五边形），可能是感兴趣的上下文演示连接。
We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended Rényi relative entropy, we then introduce a family of universal steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased b…
Many determinantal inequalities for positive definite block matrices are consequences of general entropy inequalities, specialised to Gaussian distributed vectors with prescribed covariances. In particular, strong subadditivity (SSA) yields \begin{equation*} \ln\det V_{AC} + \ln\det V_{BC} - \ln\det V_{ABC} - \ln\det V_C \geq 0 \end{equation*} for all $3\times 3$-block matrices $V_{ABC}$, where subscripts identify principal submatrices. We shall refer to the above inequality as SSA of log-det entropy. In this paper we develop further insights on the properties of the above inequality and its a…
Universal bound on the relaxation rates for quantum Markovian dynamics
本文证明任何量子信道中最大弛豫速率不超过所有弛豫速率之和除以希尔伯特空间维数，给出一个普适且紧的约束，可用于排除完全正可分演化。
Violation of Bell inequalities and Quantum Tomography with Pure-states, Werner-states and Maximally Entangled Mixed States created by a Universal Quantum Entangler
利用一种新颖的高亮度偏振纠缠光子对的通用光源，可以产生任意结构的纠缠纯态、Werner态和广义混合态，它们可以跨越2 × 2希尔伯特空间。贝尔不等式的违反已经第一次用纯态（实际上是一个概念上相关的理想条件）和沃纳态进行了检验。广义的“最大纠缠混合态”（MEMS）也是第一次合成和他们的奇异性质的量子层析技术的手段进行了研究。
We consider relations between communication complexity problems and detecting correlations (violating local realism) with no local hidden variable model. We show first universal equivalence between characteristics of protocols used in that type of problems and non-signaling correlations. We construct non linear bipartite Bell type inequalities and strong nonlocality test with binary observables by providing general method of Bell inequalities construction and showing that existence of gap between quantum and classical complexity leads to violation of these inequalities. We obtain, first to our…
Tripartite Form Universality in Holographic Entropy Inequalities
本文猜想并证明两个无限全息熵不等式族均可改写为三部分形式，提供显式表达式并推导有用恒等式，展示该形式在证明结构性质中的威力。
Convex Split Lemma without Inequalities
本文用碰撞互信息替代最大互信息，将凸分解引理从不等式改进为等式，获得更紧的量子信源编码可达界，并给出仅依赖 Rényi 熵的通用平滑最大互信息上界。
Entangled coherent states and violations of Bell-CHSH inequalities
本文利用三类纠缠相干态和无限维赝自旋算符构造Bell-CHSH不等式中的二分算符，通过计算关联函数分析参数区域，揭示了可导致不等式违背并饱和Tsirelson界的条件。
Universal chain rules from entropic triangle inequalities
该研究利用熵三角不等式证明了光滑最小熵变体的通用链式法则，推导了光滑最大熵的对应关系，还提出放宽态约束的近似熵累积定理，可用于并行设备无关量子密钥分发的安全性证明。
Probing quantum complexity via universal saturation of stabilizer entropies
本研究证明稳定子Rényi熵在非克利福德操作临界数量处饱和，呈现普适行为，并揭示其临界点依赖Rényi指数，为量子复杂性表征提供新方法。
Colbeck (Thesis, 2006) proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves the known noise tolerance for secure randomness expansion: for the commonly used CHSH game, full security was…
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