## Permutationally invariant state reconstruction

Publication: Research - peer-review › Journal article – Annual report year: 2012

### Standard

**Permutationally invariant state reconstruction.** / Moroder, Tobias; Hyllus, Philipp; Tóth, Géza; Schwemmer, Christian; Niggebaum, Alexander; Gaile, Stefanie; Gühne, Otfried; Weinfurter, Harald.

Publication: Research - peer-review › Journal article – Annual report year: 2012

### Harvard

*New Journal of Physics*, vol 14, no. 10, pp. 105001., 10.1088/1367-2630/14/10/105001

### APA

*New Journal of Physics*,

*14*(10), 105001. 10.1088/1367-2630/14/10/105001

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### MLA

*New Journal of Physics*. 2012, 14(10). 105001. Available: 10.1088/1367-2630/14/10/105001

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### Bibtex

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### RIS

TY - JOUR

T1 - Permutationally invariant state reconstruction

AU - Moroder,Tobias

AU - Hyllus,Philipp

AU - Tóth,Géza

AU - Schwemmer,Christian

AU - Niggebaum,Alexander

AU - Gaile,Stefanie

AU - Gühne,Otfried

AU - Weinfurter,Harald

PY - 2012

Y1 - 2012

N2 - Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.

AB - Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.

KW - State reconstruction, quantum tomography

KW - General statistical methods

KW - Operator theory

KW - Numerical optimization

U2 - 10.1088/1367-2630/14/10/105001

DO - 10.1088/1367-2630/14/10/105001

M3 - Journal article

VL - 14

SP - 105001

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 10

ER -