Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916585711599616 |
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| author | Hu, Lei Nomeir, Mohamed Aytekin, Alptug Shi, Yu Ulukus, Sennur Guha, Saikat |
| author_facet | Hu, Lei Nomeir, Mohamed Aytekin, Alptug Shi, Yu Ulukus, Sennur Guha, Saikat |
| contents | We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims to compute $K$ linear combinations of these data streams, represented as $Y = \mathbf{V}_1 W_1 + \mathbf{V}_2 W_2 + \cdots + \mathbf{V}_S W_S \in \mathbb{F}_d^{K \times 1}$. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error-correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC Hu, Lei Nomeir, Mohamed Aytekin, Alptug Shi, Yu Ulukus, Sennur Guha, Saikat Information Theory Networking and Internet Architecture Signal Processing Quantum Physics We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,\cdots, W_S$ over a finite field $\mathbb{F}_d$. A user aims to compute $K$ linear combinations of these data streams, represented as $Y = \mathbf{V}_1 W_1 + \mathbf{V}_2 W_2 + \cdots + \mathbf{V}_S W_S \in \mathbb{F}_d^{K \times 1}$. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error-correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases. |
| title | Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC |
| topic | Information Theory Networking and Internet Architecture Signal Processing Quantum Physics |
| url | https://arxiv.org/abs/2501.16296 |