Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements
We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/96814 https://orcid.org/0000-0002-3944-8449 |
| _version_ | 1826218168356438016 |
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| author | Li, Ke Smith, Graeme |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Li, Ke Smith, Graeme |
| author_sort | Li, Ke |
| collection | MIT |
| description | We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandao and Harrow’s de Finetti theorem where a kind of partially-one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with an amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations. |
| first_indexed | 2024-09-23T17:15:35Z |
| format | Article |
| id | mit-1721.1/96814 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:15:35Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/968142022-10-03T11:24:51Z Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements Li, Ke Smith, Graeme Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Laboratory for Nuclear Science Li, Ke We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandao and Harrow’s de Finetti theorem where a kind of partially-one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with an amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations. National Science Foundation (U.S.) (Grant CCF-1110941) National Science Foundation (U.S.) (Grant CCF-1111382) 2015-04-27T12:29:18Z 2015-04-27T12:29:18Z 2015-04 2015-02 2015-04-24T22:00:06Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/96814 Li, Ke, and Graeme Smith. “Quantum de Finetti Theorem Under Fully-One-Way Adaptive Measurements.” Physical Review Letters 114, no. 16 (April 2015). © 2015 American Physical Society https://orcid.org/0000-0002-3944-8449 en http://dx.doi.org/10.1103/PhysRevLett.114.160503 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Li, Ke Smith, Graeme Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title | Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title_full | Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title_fullStr | Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title_full_unstemmed | Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title_short | Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements |
| title_sort | quantum de finetti theorem under fully one way adaptive measurements |
| url | http://hdl.handle.net/1721.1/96814 https://orcid.org/0000-0002-3944-8449 |
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