Experimental Study of Optimal Measurements for Quantum State Tomography

Sosa-Martinez, H.; Lysne, Nathan; Baldwin, Charles; Kalev, Amir; Deutsch, Ivan; Jessen, Poul

doi:10.1103/physrevlett.119.150401

Cited by 28 publications

(15 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So, while one can pose the question of their existence using pure geometry, SICs are relevant to applied physics. Indeed, SIC measurements have recently been performed or approximated in the laboratory [27][28][29][30][31][32][33][34], and they are known to be optimal measurements for quantum-state tomography [35].…”

Section: Introductionmentioning

confidence: 99%

The SIC Question: History and State of Play

Fuchs

Hoang

Stacey

2017

Axioms

189

182

View full text Add to dashboard Cite

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.

show abstract

Section: Introductionmentioning

confidence: 99%

The SIC Question: History and State of Play

Fuchs

Hoang

Stacey

2017

Axioms

189

182

View full text Add to dashboard Cite

show abstract

“…Here, I n denotes the n-dimensional identity matrix. An active field of research has been focused on the physical implementation of POVMs [28][29][30][31][32]. One of the strategies is based on Naimark's dilation theorem.…”

Section: Povmsmentioning

confidence: 99%

Quantum Optical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain

2018

View full text Add to dashboard Cite

Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al.[1] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols.

show abstract

“…Once the measurements are complete, the reconstruction itself can be computationally intensive, as solving inverse problems is not easy. For this reason there are many ingenious approaches to reduce the number of measurements needed, or to extract as much information as possible by a judicious choice of measurement [31][32][33][34]. To return to our shadow analogy: How many projections do we need and what should they be to quickly find the object?…”

mentioning

confidence: 99%