publication . Article . Preprint . Other literature type . 2018

Volume of the space of qubit-qubit channels and state transformations under random quantum channels

Lovas, Attila; Andai, Attila;
Open Access
  • Published: 12 Oct 2018 Journal: Reviews in Mathematical Physics, volume 30, page 1,850,019 (issn: 0129-055X, eissn: 1793-6659, Copyright policy)
  • Publisher: World Scientific Pub Co Pte Lt
Abstract
The simplest building blocks for quantum computations are the qubit-qubit quantum channels. In this paper, we analyze the structure of these channels via their Choi representation. The restriction of a quantum channel to the space of classical states (i.e. probability distributions) is called the underlying classical channel. The structure of quantum channels over a fixed classical channel is studied, the volume of general and unital qubit channels with respect to the Lebesgue measure is computed and explicit formulas are presented for the distribution of the volume of quantum channels over given classical channels. We study the state transformation under unifor...
Persistent Identifiers
Subjects
arXiv: Computer Science::Information Theory
ACM Computing Classification System: Data_CODINGANDINFORMATIONTHEORYComputerSystemsOrganization_MISCELLANEOUS
free text keywords: Mathematical Physics, Quantum Physics, 81P16, 81P45, 94A17, Computation, Qubit, Quantum, Physics, Communication channel, Information geometry, Quantum mechanics, Quantum channel

[1] A. Andai. Volume of the quantum mechanical state space. Journal of Physiscs A: Mathematical and Theoretical, 39:13641-13657, 2006. [OpenAIRE]

[2] J. Bouda, M. Koniorczyk, and A. Varga. Random unitary qubit channels: entropy relations, private quantum channels and non-malleability. The European Physical Journal D, 53(3):365-372, 2009.

[3] W. Bruzda, V. Cappellini, H.-J. Sommers, and K. Zyczkowski. Random quantum operations. Physics Letters A, 373(3):320-324, 2009. [OpenAIRE]

[4] M.-D. Choi. Completely positive linear maps on complex matrices. Linear Algebra and Appl., 10:285-290, 1975.

[5] A. Harrow, P. Hayden, and D. Leung. Superdense coding of quantum states. Phys. Rev. Lett., 92(18), 2004. [OpenAIRE]

[6] A. Jamiol kowski. Linear transformations which preserve trace and positive semidefiniteness of operators. Rep. Mathematical Phys., 3(4):275-278, 1972.

[7] M. A. Neilsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000.

[8] S. Omkar, R. Srikanth, and Subhashish Banerjee. Dissipative and nondissipative single-qubit channels: dynamics and geometry. Quantum Information Processing, 12(12):3725-3744, 2013.

[9] Igor Pak. Four questions on birkhoff polytope. Annals of Combinatorics, 4(1):83-90, 2000.

[10] A. Pasieka, D. W. Kribs, R. Laflamme, and R. Pereira. On the geometric interpretation of single qubit quantum operations on the bloch sphere. Acta Appl. Math., 108(697), 2009.

[11] D. Petz. Quantum Information Theory and Quantum Statistics. Springer, Berlin-Heidelberg, 2008.

[12] M. B. Ruskai, S. Szarek, and E. Werner. An analysis of completely positive trace- preserving maps on M2. Linear Algebra Appl., 347:159-187, 2002.

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