Topic
Coherent information
About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.
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TL;DR: This work gives a bound and uses it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero and shows that the framework can be used for proving generalized bounds on the reliability.
Abstract: Information theory tells us that if the rate of sending information across a noisy channel were above the capacity of that channel, then the transmission would necessarily be unreliable. For classical information sent over classical or quantum channels, one could, under certain conditions, make a stronger statement that the reliability of the transmission shall decay exponentially to zero with the number of channel uses, and the proof of this statement typically relies on a certain fundamental bound on the reliability of the transmission. Such a statement or the bound has never been given for sending quantum information. We give this bound and then use it to give the first example where the reliability of sending quantum information at rates above the capacity decays exponentially to zero. We also show that our framework can be used for proving generalized bounds on the reliability.
133 citations
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TL;DR: In this paper, it was shown that if the loss of coherent information of the input state is small, then approximate quantum error correction is possible, but only if the channel does not decrease the coherent information.
Abstract: The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate quantum error correction is possible.
PACS: 03.67.H, 03.65.U
130 citations
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TL;DR: This paper examines recent developments regarding nonprobabilistic measures and principles of uncertainty-based information, which form a nucleus of the emerging generalized information theory.
129 citations
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TL;DR: A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory, which is applied to the case of noisy channels, with arbitrary input signal states.
Abstract: We define classical quantum multiway channels for transmission of classical information, after the previous work by Allahverdyan and Saakian (see Quantum Computing and Quantum Communications (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, vol.1509, 1999). Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon (1961) entropy with von Neumann (1955) entropy. For the single receiver case (multiple-access channel) the elect capacity region is determined. These results are applied to the case of noisy channels, with arbitrary input signal states. A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory.
128 citations
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TL;DR: Conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M are given to show examples of noisy channels such that no information can be corrected by such a scheme.
Abstract: We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give conditions for quantum or classical information (prepared in a specified input basis B) to be corrigible based on a measurement M. Based on these criteria we give examples of noisy channels such that (1) no information can be corrected by such a scheme, (2) for some basis B there is a correcting measurement M, (3) for all bases B there is an M and (4) there is a measurement M which allows perfect correction for all bases B. The last case is equivalent to the possibility of correcting quantum information, and turns out to be equivalent to the channel allowing a representation as a convex combination of isometric channels. Such channels are doubly stochastic but not conversely.
128 citations