Physical realizability of multi-level quantum systems

This paper considers the physical realizability condition for multi-level quantum systems having polynomial Hamiltonian and multiplicative coupling with respect to several interacting boson fields. Specifically, it generalizes a recent result the authors developed for two-level quantum systems. For this purpose, the algebra of SU(n) was incorporated. As a consequence, the obtained condition is given in terms of the structure constants of SU(n).

[1]  Gerard J. Milburn,et al.  Practical scheme for error control using feedback , 2004 .

[2]  P. H. W. Isz On Gell-Mann's ~.-Matrices, d- and j:Tensors, Octets, and Parametrizations of S U(3) , 1968 .

[3]  S. Lloyd,et al.  Coherent quantum feedback , 2000 .

[4]  Rainer Wawer,et al.  Quantum Networks: Dynamics of Open Nanostructures , 1998, VLSI Design.

[5]  Ian R. Petersen,et al.  Control of Linear Quantum Stochastic Systems , 2007 .

[6]  K. Parthasarathy An Introduction to Quantum Stochastic Calculus , 1992 .

[7]  Ian R. Petersen,et al.  Bounded Real Properties for a Class of Annihilation-Operator Linear Quantum Systems , 2011, IEEE Transactions on Automatic Control.

[8]  M. James,et al.  Stability, gain, and robustness in quantum feedback networks (13 pages) , 2005, quant-ph/0511140.

[9]  Matthew R. James,et al.  An Introduction to Quantum Filtering , 2006, SIAM Journal of Control and Optimization.

[10]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[11]  A. Sudbery,et al.  On Gell-Mann's λ-matrices,d- andf-tensors, octets, and parametrizations ofS U (3) , 1968 .

[12]  Ian R. Petersen,et al.  Preservation of commutation relations and physical realizability of open two-level quantum systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[14]  M. Resnikoff,et al.  MATRIX PRODUCTS AND THE EXPLICIT 3, 6, 9, AND 12-j COEFFICIENTS OF THE REGULAR REPRESENTATION OF SU(n). , 1967 .