Abstract
In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for , as a function of all involved parameters. We find in the case that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.
Highlights
In information theory, the main tasks to perform are the transmission, codification, and compression of information [1]
The mean value of the ratio is Communication enhancement is a challenging task in quantum information processing due to imperfection of communication channels subjected to depolarization
Causal order has been proposed as a disruptive procedure to improve communication, compression of quantum information, bringing the quantum possibilities into a new frontier
Summary
The main tasks to perform are the transmission, codification, and compression of information [1]. Encodes N2 ◦ N3 ◦ N1 ; (e) ρc = |5i h5| encodes N3 ◦ N1 ◦ N2 ; (f) ρc = |6i h6| encodes N3 ◦ N2 ◦ N1 ; (g) if ρc = |+i h+|, where |+i = √1 ∑6k=1 |k i we shall have a superposition of six different causal orders This is an indefinite causal order called quantum 3-switch whose input and output are ρ ⊗ ρc and S(N1 , N2 , N3 )(ρ ⊗ ρc ), respectively.
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