Quantitative verification of entanglement and fidelities from incomplete measurement data
Open accessAbstract
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires the determination of a parameter set that is growing exponentially with the number of qubits and becomes infeasible even for moderate numbers of particles. Non-trivial bounds on experimentally prepared entanglement can however be obtained from partial information on the density matrix. As introduced in the paper of K.M.R. Audenaert and M.B. Plenio [New J. Phys. 2006, 8, 266], the fundamental question is then formulated as: What is the entanglement content of the least entangled quantum state that is compatible with the available measurement data? We formulate the problem mathematically [Audenaert, K.M.R.; Plenio, M.B. New J. Phys. 2006, 8, 266] employing methods from the theory of semi-definite programming and then address this problem for the case, where the goal of the experiment is the creation of graph states. The observables that we consider are the generators of the stabilizer group, thus the number of measurement settings grows only linearly in the number of qubits. We provide analytical solutions as well as numerical methods that may be applied directly to experiments, and compare the obtained bounds with results from full-state tomography for simulated data.
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In the ideal case, detection of the two ancilla photons in the heralded CNOT occurs with probability p = 1/16 and guarantees the CNOT logic has been performed on the two photonic qubits.
“In the ideal case, the detection of the two ancilla photons, which occurs with probability p = 1 / 16, guarantees the CNOT logic has been performed on the two photonic qubits.”
From Universal linear optics (2015) · cites this paper as [32]
The heralded CNOT gate is a four-photon scheme [32] adapted for implementation with the six-mode LPU plus a seventh auxiliary coupling mode on chip.
“The heralded CNOT gate shown in Fig. 2(e), is a four-photon scheme [32] that has been adapted for implementation with the six-mode LPU, plus a seventh auxiliary coupling mode (mode 0) also contained on our chip.”
From Universal linear optics (2015) · cites this paper as [32]
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- Authors
- Wunderlich, H., & Plenio, M. B.
- Affiliations
- University of Siegen (DE)
- Imperial College London (GB)
- Corresponding author
- Wunderlich, Harald
- ORCID
- Plenio, Martin B.
- Venue
- Journal of Modern Optics
- Publisher
- Informa UK Limited
- Published
- 2009-10-20
- Volume
- 56
- Issue
- 18-19
- Pages
- 2100-2105
- ISSN
- 0950-0340 (ISSN-L)
- 1362-3044
- OpenAlex
- W1995793394
- Cited by
- 30
- References
- 14
- Citations by year
- 2020: 1 · 2019: 2 · 2017: 3 · 2016: 3 · 2015: 3 · 2014: 2 · 2013: 1 · 2012: 4
- FWCI
- 5.41
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Modern Optics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- entanglement quantification, incomplete measurement data, graph states, semidefinite programming, entanglement bounds, fidelity, multipartite entanglement
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