Prescription for experimental determination of the dynamics of a quantum black box

Abstract

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.

Robust dynamical decoupling

“…The ideal and actual processes can therefore be quantified by the matrix elements c mn . For the target evolution, the c-matrix is The matrix elements for the actual process are determined experimentally by quantum process tomography [3,100]. We use them to calculate the process fidelity from equation (3.1).…”

Realization of quantum process tomography in NMR

“…Quantum process tomography, as introduced by Chuang and Nielsen [3], can be summarized as follows. A general quantum operation on a quantum state ρ is a superoperator E, a linear, trace-preserving, completely positive map [9][10][11].…”

“…However, quantum information theory tells us that so few parameters barely even begin to represent the full dynamics which quantum systems are capable of; for example, the evolution between two fixed times of a two-level quantum system (a qubit), coupled to an arbitrary reservoir, is described by twelve real parameters [3]. For a two qubit system, this number grows to 240, and in general, for n qubits it is 16 n − 4 n .…”

“…The procedure for quantum process tomography has been described in detail in the literature [3][4][5]. It relies upon the ability to prepare a complete set of quantum states ρ j as input to the unknown process E t , and the ability to measure the density matrices of the output quantum states from the process E t (ρ).…”

NMR Quantum Information Processing

“…It allows for a comparison between different devices, and indicates the prospects of these devices with respect to the fault-tolerant quantum computing [20]. The traditional approach for characterizing any quantum process is known as quantum process tomography (QPT) [21,22], which has been realized in up to 3-qubit systems in experiment [23][24][25][26][27][28]. However an arbitrary process on a n-qubit system has (2 ) free parameters.…”