Abstract
We address the question of whether there is a way of characterizing the quantum information transport properties of a medium or material. For this analysis, the special features of quantum information have to be taken into account. We find that quantum communication over an isotropic medium, as opposed to classical information transfer, requires the transmitter to direct the signal toward the receiver. Furthermore, for large classes of media there is a threshold, in the sense that ‘sufficiently much’ of the signal has to be collected. Therefore, the medium's capacity for quantum communication can be characterized in terms of how the sizes of the transmitter and receiver have to scale with the transmission distance to maintain quantum information transmission. To demonstrate the applicability of this concept, an n-dimensional spin lattice is considered, yielding a sufficient scaling of δn/3 with the distance δ.
Highlights
The propagation of disturbances in materials, e.g., electric pulses in a piece of metal, sound in a solid, or spin-waves in a spin lattice, can be regarded as a transmission of information
To get an intuitive picture of the setting we consider one can think of radio transmission over free space, i.e., imagine a propagation medium that is translation symmetric and isotropic and that we are in control only of limited transmitter and receiver regions
While radio transmission is typically modeled as classical information transfer over a classical medium, we here consider quantum information transfer over quantum mechanical media
Summary
The propagation of disturbances in materials, e.g., electric pulses in a piece of metal, sound in a solid, or spin-waves in a spin lattice, can be regarded as a transmission of information. To get an intuitive picture of the setting we consider one can think of radio transmission over free space, i.e., imagine a propagation medium that is translation symmetric and isotropic (in a wide sense) and that we are in control only of limited transmitter and receiver regions. We suggest to characterize this quantum information transport property by how the size of the transmitter and receiver regions have to scale with increasing transmission distance in order to obtain quantum communication. For 1D spin chains it is known that perfect state transfer can be obtained by tuning the interactions locally along the chain [3] One could imagine this to be possible in higher dimensions [4]. In [5] it was shown that communication between arbitrary points can be achieved without the transmitter and receiver knowing each others positions This result assumes a finite lattice, which is excluded in our case by the effectively infinite medium. We note that the propagation of information in a medium, as studied here, is related to the LiebRobinson bound [6].‡
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