Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstructing high-dimensional two-photon entangled states via
  compressive sensing   Accurately establishing the state of large-scale quantum systems is an
important tool in quantum information science; however, the large number of
unknown parameters hinders the rapid characterisation of such states, and
reconstruction procedures can become prohibitively time-consuming. Compressive
sensing, a procedure for solving inverse problems by incorporating prior
knowledge about the form of the solution, provides an attractive alternative to
the problem of high-dimensional quantum state characterisation. Using a
modified version of compressive sensing that incorporates the principles of
singular value thresholding, we reconstruct the density matrix of a
high-dimensional two-photon entangled system. The dimension of each photon is
equal to $d= 17$, corresponding to a system of 83521 unknown real parameters.
Accurate reconstruction is achieved with approximately 2500 measurements, only
3\% of the total number of unknown parameters in the state. The algorithm we
develop is fast, computationally inexpensive, and applicable to a wide range of
quantum states, thus demonstrating compressive sensing as an effective
technique for measuring the state of large-scale quantum systems.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ