2009/06/22 by Huangjun Zhu, Yong Siah Teo, Berthold-Georg Englert +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Data mining #Dimension (graph theory) #Entanglement witness #Hilbert space #Mathematics #Measure (data warehouse) #Open quantum system #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum operation #Quantum state #Quantum tomography #Qubit #SIC-POVM #State (computer science) #Theoretical computer science #Theoretical physics #W state #Witness #quant-ph
paper · pdf · doi:10.1103/physreva.81.052339
published as Physical Review A 81 (2010) 052339 (8 pages) · 5 pages, 1 figure
arxiv created 2009/06/22 · openalex publication_date 2010/05/26 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the dimension of the state space. The witnesses can be measured successively; if all of them give an inconclusive result, one exploits their tomographic completeness for a reconstruction of the quantum state and can then determine its entanglement properties by data processing. There are witnesses that are optimal for this purpose. The optimized witness-based measurement can provide exponential improvement with respect to witness efficiency in high-dimensional Hilbert spaces, at the price of a reduction in the tomographic efficiency. We describe a systematic construction and illustrate the matter with the example of two qubits. For the case of two polarization qubits of photons, we show how existing technology can be used to implement the optimized witnesses in a very efficient way. Owing to the details of the implementation, which actually measures the eigenstate basis of the witness rather than solely determining the expectation value of the witness, one does not need to measure more than six witnesses in this example of a 16-dimensional state space.