Coding Analog of Superadditivity using Quantum Tensor Product Codes

Researchers at PNSI lab led by Prof. Garani are actively involved in the broad areas of research within quantum error correction. In a recent breakthrough work, Nadkarni and Garani demonstrated how a useful quantum code can be constructed from zero-rate entanglement-assisted CSS codes [1].

Demonstration of coding analog of superadditivity [1]:

Codes C₁[3,1,3] and C₂[3,1,3] are over Galois fields F₂ and F₄. These two codes yield zero-rate entanglement-assisted CSS codes since the number of logical qudits is zero. The tensor product of these codes yields a useful quantum code of rate 1/3, demonstrating coding analog of superadditivity.

Also, the authors in [2] have proposed a novel photonic architecture of such entanglement-assisted binary quantum tensor product codes within a quantum transceiver system [2].

References

[1] P. J. Nadkarni and S. S. Garani, “Coding analog of superadditivity using entanglement-assisted quantum tensor product codes over F_p^k,” in IEEE Transactions on Quantum Engineering, 2020. [Editor’s choice: Listed in the journal portal’s front panel]

[2] P. J. Nadkarni and S. S. Garani, “Photonic Architecture of Entanglement Assisted Binary Quantum Tensor Product Codes,” in Frontier in Optics, Washington D.C., Sep. 2019.

Website: https://eecs.iisc.ac.in/people/shayan-garani/

Faculty: Shayan Srinivasa Garani, ESE

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<span style="text-align:center;">Figure: Schematic block diagram for entanglement-assisted binary tensor product codes setup within a quantum transceiver: The error correction setup consists of the encoder, interleaver, channel, de-interleaver, error correction circuit and decoding blocks. Pre-shared entangled bits (Bell pairs) are shared between the transmitter and receiver. The circuit elements needed to implement the quantum system for each block are drawn within the corresponding blocks. For more detailed description of the quantum ECC architecture, the reader is referred to [2].</span>

Figure: Schematic block diagram for entanglement-assisted binary tensor product codes setup within a quantum transceiver: The error correction setup consists of the encoder, interleaver, channel, de-interleaver, error correction circuit and decoding blocks. Pre-shared entangled bits (Bell pairs) are shared between the transmitter and receiver. The circuit elements needed to implement the quantum system for each block are drawn within the corresponding blocks. For more detailed description of the quantum ECC architecture, the reader is referred to [2].