Multiaccess quantum communication and product higher rank numerical range

In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.--D. Choi {\it et al.}, Rep. Math. Phys. {\bf 58}, 77 (2006); Lin. Alg. Appl. {\bf 418}, 828 (2006)], is a natural tool for studying a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to other numerical ranges, which were recently introduced in the literature. Further, the concept is applied to the construction of codes for bi--unitary two--access channels with a hermitian noise model. Analytical techniques for both outerbounding the product higher rank numerical range and determining its exact shape are developed for this case. Finally, the reverse problem of constructing a noise model for a given product range is considered.

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Decoding surface code with a distributed neural network–based decoder

Quantum Machine Intelligence ◽

10.1007/s42484-020-00015-9 ◽

2020 ◽

Vol 2 (1) ◽

Cited By ~ 2

Author(s):

Savvas Varsamopoulos ◽

Koen Bertels ◽

Carmen G. Almudever

Keyword(s):

Neural Network ◽

Renormalization Group ◽

Error Correction ◽

Quantum Error Correction ◽

Noise Model ◽

Error Correction Codes ◽

Exponential Increase ◽

Main Challenge ◽

Surface Code ◽

Quantum Error

Abstract There has been a rise in decoding quantum error correction codes with neural network–based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger code distances due to an exponential increase of the error syndrome space. Note that successfully decoding the surface code under realistic noise assumptions will limit the size of the code to less than 100 qubits with current neural network–based decoders. Such a problem can be tackled by a distributed way of decoding, similar to the renormalization group (RG) decoders. In this paper, we introduce a decoding algorithm that combines the concept of RG decoding and neural network–based decoders. We tested the decoding performance under depolarizing noise with noiseless error syndrome measurements for the rotated surface code and compared against the blossom algorithm and a neural network–based decoder. We show that a similar level of decoding performance can be achieved between all tested decoders while providing a solution to the scalability issues of neural network–based decoders.

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Quantum error correction for a subgroup of the Pauli group using higher rank numerical range

Linear and Multilinear Algebra ◽

10.1080/03081087.2015.1039954 ◽

2015 ◽

Vol 64 (1) ◽

pp. 68-77

Author(s):

Sayyed Ahmad Mousavi ◽

Abbas Salemi

Keyword(s):

Error Correction ◽

Numerical Range ◽

Quantum Error Correction ◽

Higher Rank ◽

Quantum Error

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Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels

npj Quantum Information ◽

10.1038/s41534-021-00412-3 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Haowei Shi ◽

Min-Hsiu Hsieh ◽

Saikat Guha ◽

Zheshen Zhang ◽

Quntao Zhuang

Keyword(s):

Phase Modulation ◽

Multiple Access ◽

Quantum Communication ◽

Capacity Region ◽

Parametric Amplifiers ◽

Classical Communication ◽

Multiple Access Channels ◽

Squeezed Vacuum ◽

Vacuum States ◽

The One

AbstractWe solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

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