Rank lower bounds on non-local quantum computation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911073300381696 |
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| author | Asadi, Vahid R. Culf, Eric May, Alex |
| author_facet | Asadi, Vahid R. Culf, Eric May, Alex |
| contents | A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, $f$-routing and $f$-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function $f(x,y)$ in terms of the rank of a matrix $g(x,y)$ whose entries are zero when $f(x,y)=0$, and strictly positive otherwise. This also leads to a lower bound on the Schmidt rank in terms of the non-deterministic quantum communication complexity of $f(x,y)$. Because of a relationship between $f$-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18647 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rank lower bounds on non-local quantum computation Asadi, Vahid R. Culf, Eric May, Alex Quantum Physics A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, $f$-routing and $f$-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function $f(x,y)$ in terms of the rank of a matrix $g(x,y)$ whose entries are zero when $f(x,y)=0$, and strictly positive otherwise. This also leads to a lower bound on the Schmidt rank in terms of the non-deterministic quantum communication complexity of $f(x,y)$. Because of a relationship between $f$-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS. |
| title | Rank lower bounds on non-local quantum computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.18647 |