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arXiv:1812.08810 · IOP SciNotes

On quantum reading, quantum illumination, and other notions

Stefano Pirandola

Published Mar 1, 2021• 4 citations
arXivHTMLPDF

Abstract

In this brief review, we start by clarifying the crucial differences between three different protocols of quantum channel discrimination. In some recent literature, there has been confusion between the protocols of quantum illumination [ 1 , 2 ], quantum reading [ 3 ], and a scheme of communication within a discrete-variable quantum computer [ 4 ]. While all these protocols are based on the model of quantum channel discrimination, they have completely different applications and features, which is the reason why they have different names and should not be naively confused. We also discuss the notion of quantum reading capacity [ 5 ] of an ensemble of quantum channels, clarifying how this is easily extended to an adaptive formulation and discussing the mathematical conditions under which it can be connected to the different notion of dense coding capacity [ 6 ] of a quantum channel.

DOI
10.1088/2633-1357/abe99e

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In this brief review, we start by clarifying the crucial differences between three different protocols of quantum channel discrimination. In some recent literature, there has been confusion between the protocols of quantum illumination [ 1 , 2 ], quantum reading [ 3 ], and a scheme of communication within a discrete-variable quantum computer [ 4 ]. While all these protocols are based on the model of quantum channel discrimination, they have completely different applications and features, which is the reason why they have different names and should not be naively confused. We also discuss the notion of quantum reading capacity [ 5 ] of an ensemble of quantum channels, clarifying how this is easily extended to an adaptive formulation and discussing the mathematical conditions under which it can be connected to the different notion of dense coding capacity [ 6 ] of a quantum channel.
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The readout of a classical memory can be modelled as a problem of quantum channel discrimination, where a decoder retrieves information by distinguishing the different quantum channels encoded in each cell of the memory (Pirandola 2011 Phys. Rev. Lett. 106 090504). In the case of optical memories, such as CDs and DVDs, this discrimination involves lossy bosonic channels and can be remarkably boosted by the use of nonclassical light (quantum reading). Here we generalize these concepts by extending the model of memory from single-cell to multi-cell encoding. In general, information is stored in a block of cells by using a channel-codeword, i.e. a sequence of channels chosen according to a classical code. Correspondingly, the readout of data is realized by a process of 'parallel' channel discrimination, where the entire block of cells is probed simultaneously and decoded via an optimal collective measurement. In the limit of a large block we define the quantum reading capacity of the memory, quantifying the maximum number of readable bits per cell. This notion of capacity is nontrivial when we suitably constrain the physical resources of the decoder. For optical memories (encoding bosonic channels), such a constraint is energetic and corresponds to fixing the mean total number of photons per cell. In this case, we are able to prove a separation between the quantum reading capacity and the maximum information rate achievable by classical transmitters, i.e. arbitrary classical mixtures of coherent states. In fact, we can easily construct nonclassical transmitters that are able to outperform any classical transmitter, thus showing that the advantages of quantum reading persist in the optimal multi-cell scenario.
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during when a number of direct quantum coding theorems were discovered. To a considerable extent this progress is due to an interplay between the quantum communication theory and quantum information ideas related to more recent development in quantum computing. It is remarkable, however, that many probabilistic tools underlying the treatment of the quantum case have their roots, and in some cases direct prototypes, in the classical Shannon theory.