Quantum Tomography

Here we provide links to publications from both inside and outside our group that we have found helpful in the development of our tomography system. If you would like to have a single document which summarizes the majority of our theory and techniques, we suggest downloading the AMO book chapter, which should be an excellent companion to the tomography code.

AMO Book Chapter

This chapter represents the latest summary of both the theoretical foundations of our quantum tomography system and the experimental techiniques used to actually implement that system on photonic qubits. It should be the primary resource for understanding Tomography at the Kwiat lab.

amo_tomo_chapter.pdf "Photonic State Tomography". This chapter will appear in the 2005 edition of Advances in Atomic, Molecular, and Optical Physics, published by Elsevier. File Size: 692 KB.

Group Publications

Our group has published a number of works leading up to the chapter above, which we hope will continue to be useful in the future.

tomo_chapter_2004.pdf "Qubit Quantum State Tomography". This chapter appeared in the 2004 book Quantum State Estimation, published by Springer as part of the Lecture Notes in Physics Series. It is a shorter version of the chapter above with less emphasis on experimental considerations, written to emphasize usefulness for any type of qubit implementation. File Size: 312 KB.

Ancilla-assisted process tomography Phys. Rev. Lett. 90, 193601 (2003). Process tomography is similar to state tomography, except instead of characterizing a quantum state, it characterizes a quantum operation. This paper describes the use of correlated two-qubit states to perform one-qubit process tomographies.

Single Optical Qubits "Precise Creation, Characterization, and Manipulation of Single Optical Qubits", Quantum Information Computation 3, 503 (2003). A discussion of the creation and measurement of optical single qubit states.

On the measurement of qubits Phys. Rev. A 64, 052312 (2001). This is the original tomography paper that our group published at Los Alamos. It is recommended that you refer to one of the newer book chapters, as this paper is somewhat dated.

Outside Publications

There is of course a huge body of work that the greater quantum information community has provided us with which has been invaluable. Below we make a partial list of these documents, and encourage anyone who knows of other useful resources to email altepete@uiuc.edu in order to have them added to this page.

Quantum State Estimation A book containing tomography articles from groups around the world, including the second book chapter presented above. It is fairly long, and contains articles from a variety of points of view. Published by Springer as part of the Lecture Notes in Physics series.

Quantum Tomography Advances in Imaging and Electron Physics Vol. 128, p. 205-308 (2003). A large (90 page) review article published by D'Ariano, Paris, and Sacchi.

tomo_chapter_2004.pdf		"Qubit Quantum State Tomography". This chapter appeared in the 2004 book Quantum State Estimation, published by Springer as part of the Lecture Notes in Physics Series. It is a shorter version of the chapter above with less emphasis on experimental considerations, written to emphasize usefulness for any type of qubit implementation. File Size: 312 KB.
Ancilla-assisted process tomography		Phys. Rev. Lett. 90, 193601 (2003). Process tomography is similar to state tomography, except instead of characterizing a quantum state, it characterizes a quantum operation. This paper describes the use of correlated two-qubit states to perform one-qubit process tomographies.
Single Optical Qubits		"Precise Creation, Characterization, and Manipulation of Single Optical Qubits", Quantum Information Computation 3, 503 (2003). A discussion of the creation and measurement of optical single qubit states.
On the measurement of qubits		Phys. Rev. A 64, 052312 (2001). This is the original tomography paper that our group published at Los Alamos. It is recommended that you refer to one of the newer book chapters, as this paper is somewhat dated.

Quantum State Estimation		A book containing tomography articles from groups around the world, including the second book chapter presented above. It is fairly long, and contains articles from a variety of points of view. Published by Springer as part of the Lecture Notes in Physics series.
Quantum Tomography		Advances in Imaging and Electron Physics Vol. 128, p. 205-308 (2003). A large (90 page) review article published by D'Ariano, Paris, and Sacchi.