Commuting multiparty quantum observables and local compatibility

Characterizing incompatibility of quantum measurements via their Naimark extensions

We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark extension, specified by a fixed ancilla state on the same ancilla Hilbert space, that maps them to a set of commuting projective measurements (PVMs). We use our result to obtain an easily checkable sufficient condition for the compatibility of a pair of dichotomic observables in any dimension. This in turn leads to a characterization of the compatib…

Margenau-Hill 算子值测度与联合可测性

Margenau-Hill operator valued measures and joint measurability

本文基于 Margenau-Hill 对应规则构造模糊准测量算子，给出量子比特、三能级系统及双量子比特自旋可观测量联合可测的不锐度参数界，并发现不相容性随 Hilbert 空间维数增大而增强。

Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates

Obtaining the expectation value of an observable on a quantum computer is a crucial step in the variational quantum algorithms. For complicated observables such as molecular electronic Hamiltonians, a common strategy is to present the observable as a linear combination of measurable fragments. The main problem of this approach is a large number of measurements required for accurate sampling of the observable's expectation value. We consider several partitioning schemes based on grouping of commuting multi-qubit Pauli products with the goal of minimizing the number of measurements. Three main d…

Joint measurability, steering and entropic uncertainty

The notion of incompatibility of measurements in quantum theory is in stark contrast with the corresponding classical perspective, where all physical observables are jointly measurable. It is of interest to examine if the results of two or more measurements in the quantum scenario can be perceived from a classical point of view or they still exhibit non-classical features. Clearly, commuting observables can be measured jointly using projective measurements and their statistical outcomes can be discerned classically. However, such simple minded association of compatibility of measurements with …

inflation 层级和 polarization 层级对于量子双局域场景是完备的

The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario

本文证明在量子双局域场景中，量子膨胀层级在交换可观测模型下具有完备性且无需额外技术约束，并指出该技术可推广为优化算子代数多项式的完备 SDP 层级。