A direct product theorem for quantum communication complexity with applications to device-independent QKD
We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product distributions. The quantum partition or efficiency bound is a lower bound on communication complexity, a non-distributional version of which...
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| Published in: | Proceedings / annual Symposium on Foundations of Computer Science pp. 1285 - 1295 |
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| Format: | Conference Proceeding |
| Language: | English |
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IEEE
01.02.2022
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| ISSN: | 2575-8454 |
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| Abstract | We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product distributions. The quantum partition or efficiency bound is a lower bound on communication complexity, a non-distributional version of which was introduced by Laplante, Lerays and Roland (2012). For a two-input boolean function, the best result for interactive quantum communication complexity known previously was due to Sherstov (2018), who showed a direct product theorem in terms of the generalized discrepancy. While there is no direct relationship between the maximum distributional quantum partition bound for product distributions, and the generalized discrepancy method, unlike Sherstov's result, our result works for two-input functions or relations whose outputs are non-boolean as well. As an application of our result, we show that it is possible to do device-independent quantum key distribution (DIQKD) without the assumption that devices do not leak any information after inputs are provided to them. We analyze the DIQKD protocol given by Jain, Miller and Shi (2020), and show that when the protocol is carried out with devices that are compatible with several copies of the Magic Square game, it is possible to extract a linear (in the number of copies of the game) amount of key from it, even in the presence of a linear amount of leakage. Our security proof is parallel, i.e., the honest parties can enter all their inputs into their devices at once, and works for a leakage model that is arbitrarily interactive, i.e., the devices of the honest parties Alice and Bob can exchange information with each other and with the eavesdropper Eve in any number of rounds, as long as the total number of bits or qubits communicated is bounded. |
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| AbstractList | We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product distributions. The quantum partition or efficiency bound is a lower bound on communication complexity, a non-distributional version of which was introduced by Laplante, Lerays and Roland (2012). For a two-input boolean function, the best result for interactive quantum communication complexity known previously was due to Sherstov (2018), who showed a direct product theorem in terms of the generalized discrepancy. While there is no direct relationship between the maximum distributional quantum partition bound for product distributions, and the generalized discrepancy method, unlike Sherstov's result, our result works for two-input functions or relations whose outputs are non-boolean as well. As an application of our result, we show that it is possible to do device-independent quantum key distribution (DIQKD) without the assumption that devices do not leak any information after inputs are provided to them. We analyze the DIQKD protocol given by Jain, Miller and Shi (2020), and show that when the protocol is carried out with devices that are compatible with several copies of the Magic Square game, it is possible to extract a linear (in the number of copies of the game) amount of key from it, even in the presence of a linear amount of leakage. Our security proof is parallel, i.e., the honest parties can enter all their inputs into their devices at once, and works for a leakage model that is arbitrarily interactive, i.e., the devices of the honest parties Alice and Bob can exchange information with each other and with the eavesdropper Eve in any number of rounds, as long as the total number of bits or qubits communicated is bounded. |
| Author | Jain, Rahul Kundu, Srijita |
| Author_xml | – sequence: 1 givenname: Rahul surname: Jain fullname: Jain, Rahul email: rahul@comp.nus.edu.sg organization: National University of Singapore Majulab,Centre for Quantum Technologies and Department of Computer Science,Singapore,Singapore,UMI 3654 – sequence: 2 givenname: Srijita surname: Kundu fullname: Kundu, Srijita email: srijita.kundu@u.nus.edu organization: Centre for Quantum Technologies National University of Singapore Singapore,Singapore |
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| Snippet | We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity in terms of the quantum partition bound for product... |
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| SubjectTerms | Boolean functions communication complexity Complexity theory Computer science device-independence direct product Games non-local games Protocols quantum cryptography Quantum entanglement quantum key distribution Qubit |
| Title | A direct product theorem for quantum communication complexity with applications to device-independent QKD |
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