Abstract
Being extremely important resources in quantum information and computation, it is vital to efficiently detect and properly characterize entangled states. We analyze in this work the problem of entanglement detection for arbitrary spin systems. It is demonstrated how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of SO(3) representations and classical lattice walks with special constraints. Within this framework, degeneracies are naturally given by generalized Catalan numbers and determine the fraction of states that are decidedly entangled and also known to be somewhat protected against decoherence. In addition, we introduce the concept of a "sterile entanglement witness", which for large enough systems detects entanglement without affecting much the system's state. We discuss when our proposed entanglement witness can be regarded as a sterile one.
| Original language | English |
|---|---|
| Article number | 30232 |
| Journal | Scientific Reports |
| Volume | 6 |
| DOIs | |
| State | Published - 27 Jul 2016 |
| Externally published | Yes |
Bibliographical note
Funding Information:We would like to thank Yakir Aharonov, Roy Ben-Israel, Wojciech Samotij and Géza Tóth for helpful comments and discussions. E.C. was supported by Israel Science Foundation Grant No. 1311/14 and ERC AdG NLST. T.H. received funding from the grant CERN/FIS-NUC/0045/2015 and was supported by the [European Union] 7th Framework Programme (Marie Curie Actions) under grant agreements No. 269217 (UNIFY) and 317089 (GATIS) and by the German Science Foundation (DFG) within the Collaborative Research Center 676 "Particles, Strings and the Early Universe". Centro de Fisica do Porto is partially funded by the Foundation for Science and Technology of Portugal (FCT). N.I. was supported in part by the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation (Center No. 1937/12), and by a center of excellence supported by the Israel Science Foundation (grant number 1989/14).
Funding
We would like to thank Yakir Aharonov, Roy Ben-Israel, Wojciech Samotij and Géza Tóth for helpful comments and discussions. E.C. was supported by Israel Science Foundation Grant No. 1311/14 and ERC AdG NLST. T.H. received funding from the grant CERN/FIS-NUC/0045/2015 and was supported by the [European Union] 7th Framework Programme (Marie Curie Actions) under grant agreements No. 269217 (UNIFY) and 317089 (GATIS) and by the German Science Foundation (DFG) within the Collaborative Research Center 676 "Particles, Strings and the Early Universe". Centro de Fisica do Porto is partially funded by the Foundation for Science and Technology of Portugal (FCT). N.I. was supported in part by the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation (Center No. 1937/12), and by a center of excellence supported by the Israel Science Foundation (grant number 1989/14).
| Funders | Funder number |
|---|---|
| Foundation for Science and Technology of Portugal | |
| Seventh Framework Programme | |
| FP7 People: Marie-Curie Actions | 269217, 317089 |
| European Commission | |
| European Commission | CERN/FIS-NUC/0045/2015 |
| Deutsche Forschungsgemeinschaft | |
| Fundação para a Ciência e a Tecnologia | |
| Israel Science Foundation | 1311/14 |
| Planning and Budgeting Committee of the Council for Higher Education of Israel | 1937/12, 1989/14 |