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arXiv:0910.1745 · New Journal of Physics

Directed quantum communication

Johan Åberg, Stefan Hengl, Renato Renner

Published Mar 20, 2013• 4 citations
arXivHTMLPDF

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 δ n /3 with the distance δ .

DOI
10.1088/1367-2630/15/3/033025

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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 δ n /3 with the distance δ .
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Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.
We study the transmission of both classical and quantum information through all the phases of a finite XXZ spin chain. This characterizes the merit of the different phases in terms of their ability to act as a quantum wire. As far as quantum information is concerned, we need only consider the transmission of entanglement as the direct transmission of a quantum state is equivalent. The isotropic AFM spin chain is found to be the optimal point of the phase diagram for the transmission of quantum entanglement when one considers both the amount of transmitted entanglement and the velocity with which it is transmitted. However, this optimal point in the phase diagram moves to the N\'eel phase when decoherence or thermal fluctuations are taken to account. This chain may also be able to transfer classical information even when, due to a large magnitude of the noise, quantum information is not transmitted at all. For a certain range of anisotropies of the model, a curious feature is found in the flow of quantum information inside the chain, namely, a hopping mode of entanglement transfer which skips the odd-numbered sites. Our predictions will potentially be testable in several physical systems.
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Quantum information processing exploits the quantum nature of information. It offers fundamentally new solutions in the field of computer science and extends the possibilities to a level that cannot be imagined in classical communication systems. For quantum communication channels, many new capacity definitions were developed in comparison to classical counterparts. A quantum channel can be used to realize classical information transmission or to deliver quantum information, such as quantum entanglement. Here we review the properties of the quantum communication channel, the various capacity measures and the fundamental differences between the classical and quantum channels.
We consider the communication scenario where K transmitters are each connected to a common receiver with an orthogonal noiseless link. One of the transmitters has a message for the receiver, who is prohibited from learning anything in the information theoretic sense about which transmitter sends the message (transmitter anonymity is guaranteed). The capacity of anonymous communications is the maximum number of bits of desired information that can be anonymously communicated per bit of total communication. For this anonymous communication problem over a parallel channel with K transmitters and one receiver, we show that the capacity is 1/K, i.e., to communicate 1 bit anonymously, each transmitter must send a 1 bit signal. Furthermore, it is required that each transmitter has at least 1 bit correlated randomness (that is independent of the messages and is not available to the receiver) per message bit and the size of correlated randomness at all K transmitters is at least K - 1 bits per message bit.