Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-03-23-418/pdf/ |
| _version_ | 1818350557165780992 |
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| author | Ivan Šupić Daniel Cavalcanti Joseph Bowles |
| author_facet | Ivan Šupić Daniel Cavalcanti Joseph Bowles |
| author_sort | Ivan Šupić |
| collection | DOAJ |
| description | Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states. |
| first_indexed | 2024-12-13T18:23:44Z |
| format | Article |
| id | doaj.art-45a041ded95848d48f75ac9f7dc2d4c4 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-13T18:23:44Z |
| publishDate | 2021-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-45a041ded95848d48f75ac9f7dc2d4c42022-12-21T23:35:39ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-03-01541810.22331/q-2021-03-23-41810.22331/q-2021-03-23-418Device-independent certification of tensor products of quantum states using single-copy self-testing protocolsIvan ŠupićDaniel CavalcantiJoseph BowlesSelf-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.https://quantum-journal.org/papers/q-2021-03-23-418/pdf/ |
| spellingShingle | Ivan Šupić Daniel Cavalcanti Joseph Bowles Device-independent certification of tensor products of quantum states using single-copy self-testing protocols Quantum |
| title | Device-independent certification of tensor products of quantum states using single-copy self-testing protocols |
| title_full | Device-independent certification of tensor products of quantum states using single-copy self-testing protocols |
| title_fullStr | Device-independent certification of tensor products of quantum states using single-copy self-testing protocols |
| title_full_unstemmed | Device-independent certification of tensor products of quantum states using single-copy self-testing protocols |
| title_short | Device-independent certification of tensor products of quantum states using single-copy self-testing protocols |
| title_sort | device independent certification of tensor products of quantum states using single copy self testing protocols |
| url | https://quantum-journal.org/papers/q-2021-03-23-418/pdf/ |
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