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arXiv:1509.01080

Nonclassical readout of optical memories under local energy constraint

Gaetana Spedalieri, Cosmo Lupo, Stefano Pirandola

Published Sep 3, 2015• 0 citations
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Abstract

Nonclassical states of light play a central role in many quantum information protocols. Their quantum features have been exploited to improve the readout of information from digital memories, modelled as arrays of microscopic beam splitters [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of "quantum reading", a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.

DOI
10.48550/arxiv.1509.01080

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Nonclassical states of light play a central role in many quantum information protocols. Their quantum features have been exploited to improve the readout of information from digital memories, modelled as arrays of microscopic beam splitters [S. Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of "quantum reading", a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.
Nonclassical states of light play a central role in many quantum information protocols. Very recently, their quantum features have been exploited to improve the readout of information from digital memories, modeled as arrays of microscopic beam splitters [Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of ``quantum reading,'' a nonclassical source of light with Einstein-Podolski-Rosen correlations has been proven to retrieve more information than any classical source. In particular, the quantum-classical comparison has been performed under a global energy constraint, i.e., by fixing the mean total number of photons irradiated over each memory cell. In this paper we provide an alternative analysis which is based on a local energy constraint, meaning that we fix the mean number of photons per signal mode irradiated over the memory cell. Under this assumption, we investigate the critical number of signal modes after which a nonclassical source of light is able to beat any classical source irradiating the same number of signals.
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.
We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a nonclassical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have nontrivial applications in the technology of digital memories, such as optical disks and barcodes.
It has been shown recently S. Pirandola [Phys. Rev. Lett. 106, 090504 (2011)] that entangled light with Einstein-Podolsky-Rosen correlations retrieves information from digital memory better than any classical light. In identifying this, a model of digital memory with each cell consisting of a reflecting medium with two reflectivities (each memory cell encoding the binary numbers 0 or 1) is employed. The readout of binary memory essentially corresponds to discrimination of two bosonic attenuator channels characterized by different reflectivities. The model requires an entire mathematical paraphernalia of a continuous variable Gaussian setting for its analysis when arbitrary values of reflectivities $0\ensuremath{\le}{r}_{0},{r}_{1}\ensuremath{\le}1$ are considered. Here we restrict ourselves to a basic quantum readout mechanism with two different families of non-Gaussian entangled states of light, in which the binary channels to be discriminated are (i) ideal memory characterized by reflectivity r1=1{r}_{1}=1r1​=1 (identity channel) and (ii) a thermal noise channel---where the signal light illuminating the memory location gets completely lost (r0=0{r}_{0}=0r0​=0) and only a white thermal noise hitting the upper side of the memory reaches the decoder. We compare the quantum reading efficiency of two families of non-Gaussian entangled light [($m,{m}^{\ensuremath{'}}$) family of path-entangled photon states and entangled state obtained by mixing a single photon with coherent light in a 50:50 beam splitter] with any classical source of light in this model. We identify that the classes of non-Gaussian entangled transmitters studied here offer significantly better reading performance than any classical transmitters of light in the regime of low signal intensity. We also demonstrate that the ($m,{m}^{\ensuremath{'}}$) family of entangled light exhibits better reading performance than NOON states.
We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a non-classical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have non-trivial applications in the technology of digital memories, such as optical disks and barcodes.
Quantum communication theory sets the maximum rates at which information can be encoded and decoded reliably given the physical properties of the information carriers. Here we consider the problem of readout of a digital optical memory, where information is stored by means of the optical properties of the memory cells that are in turn probed by shining a laser beam on them. Interesting features arise in the regime in which the probing light has to be treated quantum mechanically. The maximum rate of reliable readout defines the quantum reading capacity, which is proven to overcome the classical reading capacity---obtained by probing with classical light---in several relevant settings. We consider a model of optical memory in which information is encoded in the (complex-valued) attenuation factor and study the effects on the reading rates of thermal and correlated noise. The latter type of noise arises when the effects of wave diffraction on the probing light beam are taken into account. We discuss the advantages of quantum reading over the classical one and show that the former is substantially more robust than the latter under thermal noise in the regime of low power per pulse.