相关论文: Uncertainties of genuinely incompatible triple mea…
Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
We consider pairs of quantum observables (POVMs) and analyze the relation between the notions of non-disturbance, joint measurability and commutativity. We specify conditions under which these properties coincide or differ---depending for…
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
Measurement in quantum mechanics is notoriously unpredictable. The uncertainty in quantum measurement can arise from the noncommutativity between the state and the measurement basis which is intrinsically quantum, but it may also be of…
Joint measurements of non-commuting observables are characterized by unavoidable measurement uncertainties that can be described in terms of the error statistics for input states with well-defined values for the target observables. However,…
Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the…
Quantum measurements based on mutually unbiased bases (MUB) play crucial roles in foundational studies and quantum information processing. It is known that there exist inequivalent MUB, but little is known about their operational…
Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general…
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of…
Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from…
Heisenberg's measurement uncertainty relations (MUR) of two quantum observables are essential for contemporary researches in quantum foundations and quantum information science. Going beyond, here we report the first experimental test of…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
Modern coordinate measurement machines (CMM) are universal tools to measure geometric features of complex three-dimensional workpieces. To use them as reliable means of quality control, the suitability of the device for the specific…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to…
The necessary and sufficient criteria for violating the Mermin and Svetlichny inequalities by arbitrary three-qubit states are presented. Several attempts have been made, earlier, to find such criteria, however, those extant criteria are…
We formulate the accuracy of quantum measurement for a qubit system in terms of a 3 by 3 matrix. This matrix, which we refer to as the accuracy matrix, can be calculated from a positive operator-valued measure (POVM) corresponding to the…