Efficient and feasible state tomography of quantum many-body systems
| Autor: | Ohliger, M., Nesme, V., Eisert, J. |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | New J. Phys. 15, 015024 (2013) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1367-2630/15/1/015024 |
| Popis: | We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments. Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice systems |
| Databáze: | arXiv |
| Externí odkaz: |
|