Local quantum overlapping tomography
- URL: http://arxiv.org/abs/2112.03924v3
- Date: Tue, 7 Feb 2023 09:33:50 GMT
- Title: Local quantum overlapping tomography
- Authors: Bruna G. M. Ara\'ujo, M\'arcio M. Taddei, Daniel Cavalcanti, Antonio
Ac\'in
- Abstract summary: Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size.
A paradigmatic example is a scenario where one aims at determining all the reduced states only up to a given size.
Overlapping tomography provides constructions to address this problem with a number of product measurements much smaller than what is obtained when performing independent tomography of each reduced state.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Reconstructing the full quantum state of a many-body system requires the
estimation of a number of parameters that grows exponentially with system size.
Nevertheless, there are situations in which one is only interested in a subset
of these parameters and a full reconstruction is not needed. A paradigmatic
example is a scenario where one aims at determining all the reduced states only
up to a given size. Overlapping tomography provides constructions to address
this problem with a number of product measurements much smaller than what is
obtained when performing independent tomography of each reduced state. There
are however many relevant physical systems with a natural notion of locality
where one is mostly interested in the reduced states of neighboring particles.
In this work, we study this form of local overlapping tomography. First of all,
we show that, contrary to its full version, the number of product-measurement
settings needed for local overlapping tomography does not grow with system
size. Then, we present strategies for qubit and fermionic systems in selected
lattice geometries. The developed methods find a natural application in the
estimation of many-body systems prepared in current quantum simulators or
quantum computing devices, where interactions are often local.
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