Optimality of T-gate for generating magic resource

In the stabilizer formalism of fault-tolerant quantum computation,stabilizer states serve as classical objects,while magic states(non-stabilizer states)are a kind of quantum resource(called magic resource)for promoting stabilizer circuits to universal quantum computation.In this framework,the T-gate is widely used as a non-Clifford gate which generates magic resource from stabilizer states.A natural question arises as whether the T-gate is in some sense optimal for generating magic resource.We address this issue by employing an intuitive and computable quantifier of magic based on characteristic functions(Weyl transforms)of quantum states.We demonstrate that the qubit T-gate,as well as its qutrit extension,the qutrit T-gate,are indeed optimal for generating magic resource among the class of diagonal unitary operators.Moreover,up to Clifford equivalence,the T-gate is essentially the only gate having such an optimal property.This reveals some intrinsic optimal features of the T-gate.We further compare the T-gate with general unitary gates for generating magic resource.

Separability criteria based on a class of symmetric measurements

Highly symmetric quantum measurements,such as mutually unbiased measurements(MUMs)and general symmetric informationally complete positive-operator-valued measures(GSICPOVMs),play an important role in both foundational and practical aspects of quantum information theory.Recently,a broad class of symmetric measurements were introduced[K Siudzińska,(2022)Phys.Rev.A 105,042209],which can be viewed as a common generalization of MUMs and GSIC-POVMs.In this work,the role of these symmetric measurements in entanglement detection is studied.More specifically,based on the correlation matrices defined via(informationally complete)symmetric measurements,a separability criterion for arbitrary dimensional bipartite systems is proposed.It is shown that the criterion is stronger than the method provided by Siudzińska,meanwhile,it can unify several popular separability criteria based on MUMs or GSIC-POVMs.Furthermore,using these(informationally complete)symmetric measurements,two efficient criteria are presented to detect the entanglement of tripartite quantum states.The detection power and advantages of these criteria are illustrated through several examples.

玻色场中量子态的非Gauss性

在连续变量的量子信息理论中,玻色场中量子态的非Gauss性是一种重要的资源.近十年来,人们引进了多种基于距离和相对熵的非Gauss性度量,用来刻画非Gauss性的不同侧面.由于Gauss量子态的集合在辛变换所对应的酉操作下具有不变性,因此,我们希望非Gauss性的度量也具有这种辛变换下的不变性.基于Gauss态正好是一类量子不确定性关系的最小不确定性态,本文提出一个具有辛不变性的非Gauss性度量并揭示其基本性质.对玻色场中的一些重要量子态,本文计算其非Gauss性.

From wave-particle duality to wave-particle-mixedness triality:an uncertainty approach

The wave-particle duality,as a manifestation of Bohr’s complementarity,is usually quantified in terms of path predictability and interference visibility.Various characterizations of the wave-particle duality have been proposed from an operational perspective,most of them are in forms of inequalities,and some of them are expressed in forms of equalities by incorporating entanglement or coherence.In this work,we shed different insights into the nature of the wave-particle duality by casting it into a form of information conservation in a multi-path interferometer,with uncertainty as a unified theme.More specifically,by employing the simple yet fundamental concept of variance,we establish a resolution of unity,which can be interpreted as a complementarity relation among wave feature,particle feature,and mixedness of a quantum state.This refines or reinterprets some conventional approaches to wave-particle duality,and highlights informational aspects of the issue.The key idea of our approach lies in that a quantum state,as a Hermitian operator,can also be naturally regarded as an observable,with measurement uncertainty(in a state)and state uncertainty(in a measurement)being exploited to quantify particle feature and wave feature of a quantum state,respectively.These two kinds of uncertainties,although both are defined via variance,have fundamentally different properties and capture different features of a state.Together with the mixedness,which is a kind of uncertainty intrinsic to a quantum state,they add up to unity,and thus lead to a characterization of the waveparticle-mixedness complementarity.This triality relation is further illustrated by examples and compared with some popular wave-particle duality or triality relations.

Quantifying nonclassicality of multimode bosonic fields via skew information

We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information.The fundamental properties of the quantifier such as convexity,superadditivity,monotonicity,and conservation relations are revealed.The quantifier is illustrated by a variety of typical examples,and applications to the quantification of nonclassical correlations are discussed.Various extensions are indicated.

Revealing nonclassicality via s-ordered phase-space distribution

Nonclassical states play a crucial role in both theoretical and experimental investigations of quantum optics, and there is a wide interest in characterization and quantification of nonclassicality. By exploiting the freedom of the parameter s in the s-ordered phase-space distribution introduced by Cahill and Glauber [Phys. Rev. 177, 1882(1969)], we develop a method to reveal and quantify optical nonclassicality via the divided difference of the s-ordered phase-space distribution. Our approach yields naturally a family of quantifiers of optical nonclassicality, which have many desirable properties such as convexity and monotonicity under the Gaussian noise channels. The quantifiers are illustrated by evaluating nonclassicality of several typical states. Two simple and convenient criteria for nonclassicality are established, which in particular certify all nonclassical Gaussian states.

On Wick product of generalized operators

Fundamental properties of Wick product of generalized operators are investigated. The annihilation and creation algebras are characterized from various points of view. Wick ordering widely used in quantum physics is interpreted as the Wick product of generalized operators.

Generalized Fourier-Mehler transforms on white noise functional spaces

A new (non-unitary) representation of the general linear group of white noise space on Hida’s test and distribution spaces is presented. The relevant representative operators are natural generalization of Fourier-Mehler transforms.