Quantum confusion

Jean Bricmont

Sk Asfaq Hossain, Angshuman Bhattacharya

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.

Krisztina Tolotti, Riley Blank-Matthews, Arthur J. Parzygnat

The joint expectation values of quantum observables measured by two parties typically depend on the causal structure of the measurement protocol. The two causal structures we investigate here are the direct-cause scenario, in which a single quantum state is measured twice in series with a general quantum channel between measurements, and the common-cause scenario, in which a shared bipartite quantum state is measured in parallel. Through a variety of examples of qubit channels with tunable parameters, we identify the full set of input states where the direct-cause joint expectation values of Pauli observables coincide with those obtained from a common cause, a situation that we call causal confusion. More generally, for arbitrary finite-dimensional quantum systems and light-touch observables, we prove that a channel exhibits causal confusion for some input state if and only if it is a positive-partial-transpose (PPT) channel, thereby endowing PPT channels with a new operational meaning in terms of causal confusion. Using this result, we characterize the set of qubit channels for which there exists an input state leading to causal confusion as the set of entanglement-breaking channels.

The theory of quantum mechanics is a confusing beast.

LI Jingya,YU Wenbin,LIU Wenjie,WANG Jinwei

In view of the lack of effective coding schemes for quantum zero-error channel,based on the characteristics of quantum five-symbol confusion channel model and the theory of matrix theory,a coding method of five-symbol confusion channel combining quantum superposition state zero-error coding is proposed.In order to improve the channel capacity and reduce the algorithm complexity,zero-error coding is performed by using the isomorphism relationship between quantum superposition states and vectors and between channels and matrices.Analysis results show that this method has higher channel capacity and coding efficiency than the classical confusion channel coding method.