The computational two-way quantum capacity
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918299359510528 |
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| author | Meyer, Johannes Jakob Rizzo, Jacopo Raza, Asad Leone, Lorenzo Jerbi, Sofiene Eisert, Jens |
| author_facet | Meyer, Johannes Jakob Rizzo, Jacopo Raza, Asad Leone, Lorenzo Jerbi, Sofiene Eisert, Jens |
| contents | Quantum channel capacities are fundamental to quantum information theory. Their definition, however, does not limit the computational resources of sender and receiver. In this work, we initiate the study of computational quantum capacities. These quantify how much information can be reliably transmitted when imposing the natural requirement that en- and decoding have to be computationally efficient. We focus on the computational two-way quantum capacity and showcase that it is closely related to the computational distillable entanglement of the Choi state of the channel. This connection allows us to show a stark computational capacity separation. Under standard cryptographic assumptions, there exists a quantum channel of polynomial complexity whose computational two-way quantum capacity vanishes while its unbounded counterpart is nearly maximal. More so, we show that there exists a sharp transition in computational quantum capacity from nearly maximal to zero when the channel complexity leaves the polynomial realm. Our results demonstrate that the natural requirement of computational efficiency can radically alter the limits of quantum communication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The computational two-way quantum capacity Meyer, Johannes Jakob Rizzo, Jacopo Raza, Asad Leone, Lorenzo Jerbi, Sofiene Eisert, Jens Quantum Physics Computational Complexity Cryptography and Security Information Theory Quantum channel capacities are fundamental to quantum information theory. Their definition, however, does not limit the computational resources of sender and receiver. In this work, we initiate the study of computational quantum capacities. These quantify how much information can be reliably transmitted when imposing the natural requirement that en- and decoding have to be computationally efficient. We focus on the computational two-way quantum capacity and showcase that it is closely related to the computational distillable entanglement of the Choi state of the channel. This connection allows us to show a stark computational capacity separation. Under standard cryptographic assumptions, there exists a quantum channel of polynomial complexity whose computational two-way quantum capacity vanishes while its unbounded counterpart is nearly maximal. More so, we show that there exists a sharp transition in computational quantum capacity from nearly maximal to zero when the channel complexity leaves the polynomial realm. Our results demonstrate that the natural requirement of computational efficiency can radically alter the limits of quantum communication. |
| title | The computational two-way quantum capacity |
| topic | Quantum Physics Computational Complexity Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2601.15393 |