Detection and quantification of entanglement with measurement-device-independent and universal entanglement witness

Entanglement is the key resource in quantum information processing,and an entanglement witness(EW)is designed to detect whether a quantum system has any entanglement.However,prior knowledge of the target states should be known first to design a suitable EW,which weakens this method.Nevertheless,a recent theory shows that it is possible to design a universal entanglement witness(UEW)to detect negative-partial-transpose(NPT)entanglement in unknown bipartite states with measurement-device-independent(MDI)characteristic.The outcome of a UEW can also be upgraded to be an entanglement measure.In this study,we experimentally design and realize an MDI UEW for two-qubit entangled states.All of the tested states are well-detected without any prior knowledge.We also show that it is able to quantify entanglement by comparing it with concurrence estimated through state tomography.The relation between them is also revealed.The entire experimental framework ensures that the UEW is MDI.

Detecting high-dimensional multipartite entanglement via some classes of measurements

Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measure- ments are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite sys- tems of subsystems with different dimensions. It is proved that these criteria can detect the k-nonseparability （k is even） of multipartite qudit systems and arbitrary high dimensional multipartite systems of m subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.

Super-resolution and super-sensitivity of entangled squeezed vacuum state using optimal detection strategy

Interference metrology is a method for achieving high precision detection by phase estimation. The phase sensitivity of a traditional interferometer is subject to the standard quantum limit, while its resolution is constrained by the Rayleigh diffraction limit. The resolution and sensitivity of phase measurement can be enhanced by using quantum metrology. We propose a quantum interference metrology scheme using the entangled squeezed vacuum state, which is obtained using the magic beam splitter, expressed as ｜ψ〉=（｜ξ〉｜0〉＋｜0〉｜ξ〉）/√2＋2/coshr, such as the N00 N state. We derive the phase sensitivity and the resolution of the system with Z detection, project detection, and parity detection. By simulation and analysis, we determine that parity detection is an optimal detection method, which can break through the Rayleigh diffraction limit and the standard quantum limit.

Experimental detection of quantum entanglement

In this review, we introduce some methods for detecting or measuring entanglement. Several non- linear entanglement witnesses are presented. We derive a series of Bell inequalities whose maximally violations for any multipartite qubit states can be calculated by using our formulas. Both the non- linear entanglement witnesses and the Bell inequalities can be operated experimentally. Thus they supply an effective way for detecting entanglement. We also introduce some experimental methods to measure the entanglement of formation, and the lower bound of the convex-roof extension of negativity.

Lecture notes on quantum entanglement:From stabilizer states to stabilizer channels

We study mathematical,physical and computational aspects of the stabilizer formalism arising in quantum information and quantum computation.The measurement process of Pauli observables with its algorithm is given.It is shown that to detect genuine entanglement we need a full set of stabilizer generators and the stabilizer witness is coarser than the GHZ(Greenberger-Horne-Zeilinger)witness.We discuss stabilizer codes and construct a stabilizer code from a given linear code.We also discuss quantum error correction,error recovery criteria and syndrome extraction.The symplectic structure of the stabilizer formalism is established and it is shown that any stabilizer code is unitarily equivalent to a trivial code.The structure of graph codes as stabilizer codes is identified by obtaining the respective stabilizer generators.The distance of embeddable stabilizer codes in lattices is obtained.We discuss the Knill-Gottesman theorem,tableau representation and frame representation.The runtime of simulating stabilizer gates is obtained by applying stabilizer matrices.Furthermore,an algorithm for updating global phases is given.Resolution of quantum channels into stabilizer channels is shown.We discuss capacity achieving codes to obtain the capacity of the quantum erasure channel.Finally,we discuss the shadow tomography problem and an algorithm for constructing classical shadow is given.

Detecting entanglement of quantum channels

Entanglement is the crucial resource for different quantum information processing tasks.While conventional studies focus on the entanglement of bipartite or multipartite quantum states,recent works have extended the scenario to the entanglement of quantum channels,an operational quantification of the channel entanglement manipulation capability.Based on the recently proposed channel entanglement resource framework,here we study a further task of resource detection—witnessing entanglement of quantum channels.We first introduce the general framework and show how channel entanglement detection is related to the Choi state of the channel,enabling channel entanglement detection via conventional state entanglement detection methods.We also consider entanglement of multipartite quantum channels and use the stabilizer formalism to construct entanglement witnesses for circuits consisting of controlled-Z gates.We study the effectiveness of the proposed detection methods and compare their performance for several typical channels.Our work paves the way for systematic theoretical studies of channel entanglement and practical benchmarking of noisy intermediate scaled quantum devices.

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.