Petz recovery versus matrix reconstruction
Abstract
The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to local operations. We compare two different methods for obtaining the original state from the state resulting from the action of these operations. The first method involves quantum operations called Petz recovery maps, acting locally on the two subsystems. The second method is called matrix (or state) reconstruction and involves local, linear maps that are not necessarily completely positive. Moreover, we compare the quantities on which the maps employed in the two methods depend. We show that any state that admits Petz recovery also admits state reconstruction. However, the latter is successful for a strictly larger set of states. We also compare these methods in the context of a finite spin chain. Here, the state of a finite spin chain is reconstructed from the reduced states of a few neighbouring spins. In this setting, state reconstruction is the same as the matrix product operator reconstruction proposed by Baumgratz et al. [Phys. Rev. Lett. 111, 020401 (2013)]. Finally, we generalize both these methods so that they employ long-range measurements instead of relying solely on short-range correlations embodied in such local reduced states. Long-range measurements enable the reconstruction of states which cannot be reconstructed from measurements of local few-body observables alone and hereby we improve existing methods for quantum state tomography of quantum many-body systems.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 01, 2018
- Source ID
- 10.1063/1.5009658
Entities
People
- Marcus Cramer
- Martin B. Plenio
- Milan Holzäpfel
- Nilanjana Datta
Organizations
- Alexander von Humboldt Foundation
- Army Research Office
- FP7 Ideas: European Research Council
- Federal Ministry of Research, Technology and Space
- German Research Foundation
- Leibniz Universität
- Ulm University
- University of Cambridge