Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables
- 7 June 2016
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 116 (23), 230501
- https://doi.org/10.1103/physrevlett.116.230501
Abstract
Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the -symmetric extendibility.
Keywords
Funding Information
- Natural Sciences and Engineering Research Council of Canada
- Industry Canada
- Canadian Institute for Advanced Research
- National Natural Science Foundation of China (11175094, 91221205, 11425523, 11375167)
- National Basic Research Program of China (2015CB921002, 2013CB921801, 2014CB848700)
This publication has 37 references indexed in Scilit:
- Efficient quantum state tomographyNature Communications, 2010
- Quantum entanglementReviews of Modern Physics, 2009
- Entanglement detectionPhysics Reports, 2009
- Estimating Entanglement Measures in ExperimentsPhysical Review Letters, 2007
- Direct Measurement of Nonlinear Properties of Bipartite Quantum StatesPhysical Review Letters, 2005
- Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithmsJournal of Magnetic Resonance, 2004
- Method for Direct Detection of Quantum EntanglementPhysical Review Letters, 2002
- Distinguishing Separable and Entangled StatesPhysical Review Letters, 2002
- Entanglement of Formation for Isotropic StatesPhysical Review Letters, 2000
- Reduction criterion of separability and limits for a class of distillation protocolsPhysical Review A, 1999