Direct Characterization of Quantum Dynamics: I. General Theory

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  • 5 January 2006
Abstract
Experiments are always conducted on ``open'' systems, i.e., systems that interact with an external environment. The characterization of the dynamics of open quantum systems is a fundamental and central problem in quantum mechanics. Algorithms for performing this task are known as quantum process tomography, and typically rely on subjecting a complete set of quantum input states to the same open system dynamics. The corresponding output states are measured via a process known as quantum state tomography. Here we present an optimal algorithm for complete and direct characterization of quantum dynamics, which does not require quantum state tomography. We demonstrate a quadratic advantage in the number of ensemble measurements over all previously known quantum process tomography algorithms, and prove that this is optimal. As an application of our algorithm, we demonstrate that for a two-level quantum system that undergoes a sequence of amplitude damping and phase damping processes, the relaxation time T_1 and the dephasing time T_2 can be simultaneously determined via a single measurement. Moreover, we show that generalized quantum superdense coding can be implemented optimally using our algorithm. We argue that our algorithm is experimentally implementable in a variety of prominent quantum information processing systems, and show explicitly how the algorithm can be physically realized in photonic systems with present day technology. In this paper we present the general theory. In a sequel paper we provide detailed proofs for the case of qudits.

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