Abstract
Quantum turbo codes (QTC) have shown excellent error correction capabilities in the setting of quantum communication, achieving a performance less than 1 dB away from their corresponding hashing bounds. Decoding for QTCs typically assumes that perfect knowledge about the channel is available at the decoder. However, in realistic systems, such information must be estimated, and thus, there exists a mismatch between the true channel information and the estimated one. In this article, we first heuristically study the sensitivity of QTCs to such mismatch. Then, existing estimation protocols for the depolarizing channel are presented and applied in an off-line manner to provide bounds on how the use of off-line estimation techniques affects the error correction capabilities of QTCs. Finally, we present an on-line estimation method for the depolarizing probability, which, different from off-line estimation techniques, neither requires extra qubits, nor increases the latency. The application of the proposed method results in a performance similar to that obtained with QTCs using perfect channel information, while requiring less stringent conditions on the variability of the channel than off-line estimation techniques.
Highlights
Quantum turbo codes have been demonstrated to be a promising family of quantum error correction codes (QECC) with performances as close as 0.3 dB to their hashing bounds
The remainder of this paper is organized as follows: Section 2 presents the depolarizing channel and the Quantum turbo codes (QTC) system model; Section 3 presents the sensitivity of the QTC decoder with respect to the depolarizing probability mismatch; Section 4 presents existing off-line estimation methods for the depolarizing channel and obtains bounds for the performance of QTCs when such estimators are applied; Section 4 describes the proposed on-line estimation method and investigates its resulting performance; Section 5 provides the conclusions reached in this paper
We studied the performance sensitivity of QTCs applied over depolarizing channels when there exists a mismatch between the actual depolarizing probability and the probability fed to the decoders
Summary
Quantum turbo codes have been demonstrated to be a promising family of quantum error correction codes (QECC) with performances as close as 0.3 dB to their hashing bounds. It turns out that inner encoders that have those two properties are the key for QTCs in order to show a minimum distance that grows linearly with the blocklength, and a decoding algorithm that achieves convergence The application of this technique narrowed the gap that the QTCs present with respect to their hashing bounds and made them one of the most promising families of QECCs. Since the field of turbo codes in the quantum paradigm has been extensively studied, starting from the usage of extrinsic information transfer (EXIT) chart techniques by Babar et al. For serial turbo codes, the errors are not as evenly spread as the channel information is just used in the inner decoding stage This strongly suggests that (serially concatenated) QTCs will be more sensitive to depolarizing probability mismatch. The remainder of this paper is organized as follows: Section 2 presents the depolarizing channel and the QTC system model; Section 3 presents the sensitivity of the QTC decoder with respect to the depolarizing probability mismatch; Section 4 presents existing off-line estimation methods for the depolarizing channel and obtains bounds for the performance of QTCs when such estimators are applied; Section 4 describes the proposed on-line estimation method and investigates its resulting performance; Section 5 provides the conclusions reached in this paper
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