On the Significance of Quasi-Probability in Quantum Mechanics

N M Monyonko, L G Wori– Baraja, Manjit Kumar

教紀 福田, カズキ フクダ, Kazuki Fukuda

We present a theoretical study of quasi-probability based on the weak value and weak measurement with an aim to show its significance in quantum mechanics.First, we consider the general aspects of the quasi-probability underlying the weak value, which can be determined from the weak value up to a certain ambiguity parameterized by a complex number.We argue the legitimacy and the usefulness

Patrick Suppes

Abner Shimony

Christopher Ferrie, Joseph Emerson

Several finite-dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted dimensions and their physical significance in contexts such as drawing quantum-classical comparisons is limited by the non-uniqueness of the particular representation. Here we show how the mathematical theory of frames provides a unified formalism which accommodates all known quasi-probability representations of finite-dimensional quantum systems. Moreover, we show that any quasi-probability representation is equivalent to a frame representation and then prove that any such representation of quantum mechanics must exhibit either negativity or a deformed probability calculus.

Christopher Ferrie

Several finite dimensional quasi-probability representations of \nquantum states have been proposed to study various problems in \nquantum information theory and quantum foundations. These \nrepresentations are often defined only on restricted dimensions and \ntheir physical significance in contexts such as drawing \nquantum-classical comparisons is limited by the non-uniqueness of \nthe particular representation. In this thesis it is shown how the mathematical \ntheory of frames provides a unified formalism which accommodates all \nknown quasi-probability representations of finite dimensional \nquantum systems. \n \nIt is also shown that any quasi-probability \nrepresentation is equivalent to a frame representation and it is \nproven that any such representation of quantum mechanics must exhibit \neither negativity or a deformed probability calculus. \n \nAlong the way, the connection between negativity and two other famous notions of non-classicality, namely contextuality and nonlocality, is clarified.