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arXiv:2111.11135 · Entropy

Error Probability Mitigation in Quantum Reading Using Classical Codes

Francisco Revson F. Pereira, Stefano Mancini

Published Dec 21, 2021• 1 citation
arXivHTMLPDF

Abstract

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. In conjunction with the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken into consideration. The encoding and measurement schemes are connected by the probing step. As probes, we consider coherent states. In such a simple manner, interesting results are obtained. As we show, there is a threshold below which using codes surpass optimal and sophisticated schemes for any fixed rate and code. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in quantum reading.

DOI
10.3390/e24010005

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A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed-Solomon codes, BCH codes, and Reed-Muller codes. In conjunction with the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken into consideration. The encoding and measurement schemes are connected by the probing step. As probes, we consider coherent states. In such a simple manner, interesting results are obtained. As we show, there is a threshold below which using codes surpass optimal and sophisticated schemes for any fixed rate and code. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in quantum reading.
Quantum readout provides a general framework for formulating statistical discrimination of quantum channels. Several paths have been taken for such this problem. However, there is much to be done in the avenue of optimizing channel discrimination using classical codes. At least two open questions can be pointed out: how to construct low complexity encoding schemes that are interesting for channel discrimination and, more importantly, how to develop capacity-achieving protocols. This paper aims at presenting a solution to these questions using polar codes. Firstly, we characterize the information rate and reliability parameter of the channels under polar encoding. We also show that the error probability of the scheme proposed decays exponentially with the square root of the code length. Secondly, an analysis of the optimal quantum states to be used as probes is given.
Quantum reading provides a general framework to formulate the statistical discrimination of quantum channels. Applying classical codes to this task gives at least two open questions: how to construct low complexity encoding schemes that are interesting for channel discrimination and, how to develop capacity-achieving protocols. The aim of this paper is to present a solution to these questions using polar codes. We characterize the rate and reliability of the channels under polar encoding. Additionally, it is shown that the error probability of the proposed scheme decays exponentially with respect to the code length. A full version of this paper is accessible at https://arxiv.org/abs/2012.07198v2
The necessity for quantum error correction arises from the need to safeguard quantum information from errors induced by decoherence and other noise forms. However, the optimal decoding of quantum error-correcting codes is a computationally challenging task. In our research, we introduce an ensemble decoder that amalgamates the advantages of various decoders to attain lower logical error rates and the capability to decode multiple errors. We employed statistical methodologies to allocate a specific error syndrome to the decoder with the highest likelihood of accurate decoding. We applied diverse variants of the Noise model to simulate the impact of noise on transmitted quantum states accurately. The efficacy of the ensemble decoder was assessed in both Symmetric and Asymmetric Noise Models. In the Symmetric Noise Model, bit-flip and phase-flip errors are presumed to have equal probabilities, while in the Asymmetric Noise Model, these probabilities can vary. The comparison aimed to evaluate the ensemble decoder's proficiency in rectifying these error types compared to traditional decoding techniques. Our results indicate that the ensemble decoder surpasses conventional decoders in the Symmetric Noise model, particularly for higher code distances. It is also apparent that augmenting the lattice size diminishes the logical error rate and that threshold and pseudo-threshold values escalate with incremental changes in noise asymmetry. The study's findings underscore the substantial potential of the ensemble decoder in quantum error correction and communication realms.
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief introduction to the main theoretical formalism employed in the rest of the thesis, i.e., continuous-variable Quantum Information Theory and Quantum Communication Theory, we consider several decoding schemes. First, we treat the problem from an abstract perspective, presenting a method to decompose any quantum measurement into a sequence of easier nested measurements through a binary-tree search. Furthermore we show that this decomposition can be used to build a capacity-achieving decoding protocol for classical communication on quantum channels and to solve the optimal discrimination of some sets of quantum states. These results clarify the structure of optimal quantum measurements, showing that it can be recast in a more operational and experimentally-oriented fashion. Second, we consider a more practical approach and describe three receiver structures for coherent states of the electromagnetic field with applications to single-mode state discrimination and multi-mode decoding at the output of a quantum channel. We treat the problem bearing in mind the technological limitations faced nowadays in the field of optical communications: we evaluate the performance of general decoding schemes based on such technology and report increased performance of two schemes, the first one employing a non-Gaussian transformation and the second one employing a code tailored to be read out easily by the most common detectors. Eventually we characterize a large class of multi-mode adaptive receivers based on common technological resources, obtaining a no-go theorem for their capacity.
We propose a general framework for noncoherent communication using techniques from the field of quantum error correction (QEC). We first propose an approach for analyzing a classical communication channel as a quantum channel, and develop an extension of the QEC conditions to the classical case. We derive a quantum analogue of the noncoherent multiantenna wireless channel. Restricting to the case in which the number of transmitter and receiver antennas are equal and a power of two, we use the framework to develop a family of space-time block codes for noncoherent multiple-input multiple-output (MIMO) communication. Under a Rayleigh fading assumption, we derive the optimal decoder and bound the probability of symbol detection error. We compare our performance to comparable coherent and noncoherent approaches and achieve competitive performance for various antenna geometries and rates.