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Full-Text Articles in Physics
The Operational Choi-Jamio Lkowski Isomorphism, Emily Adlam
The Operational Choi-Jamio Lkowski Isomorphism, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded …
Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte
Noncontextuality Inequalities From Antidistinguishability, Matthew S. Leifer, Cristhiano Duarte
Mathematics, Physics, and Computer Science Faculty Articles and Research
Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for the …