Abstract
We have developed an enhanced technique for characterizing quantum optical processes based on probing unknown quantum processes only with coherent states. Our method substantially improves the original proposal (Lobino et al 2008 Science 322 563), which uses a filtered Glauber–Sudarshan decomposition to determine the effect of the process on an arbitrary state. We introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state. This relation eliminates the need to invoke the Glauber–Sudarshan representation for states; hence, it dramatically simplifies the task of process identification and removes a potential source of error. The new relation also enables straightforward extensions of the method to multi-mode and non-trace-preserving processes. We illustrate our formalism with several examples, in which we derive analytic representations of several fundamental quantum optical processes in the Fock basis. In particular, we introduce photon-number cutoff as a reasonable physical resource limitation and address resource versus accuracy trade-off in practical applications. We show that the accuracy of process estimation scales inversely with the square root of photon-number cutoff.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Quantum technologies employ components that transform quantum inputs to quantum or classical outputs. For example, quantum memory should be an identity map that aims to preserve input states and release them on demand. Process tomography is a practical procedure for characterizing such processes with as few assumptions as possible. Quantum optical process tomography enables full characterization using only coherent states of light produced by a standard laser source and homodyne detection of output states.
Main results. Although quantum process tomography with coherent state inputs works, the required numerical calculation is slow, involves unavoidable approximations and has not been generalized to multi-mode processes. Here, we introduce a new method based on the Fock representation rather than using the Glauber–Sudarshan decomposition, and our approach is relatively faster than the original coherent state tomography to calculate numerically, eliminates unnecessary approximations—while offering simpler error/resource analysis—and is readily generalized to the multi-mode case as well as to conditional processes.
Wider implications. Our result makes coherent-state quantum process tomography easier to implement and more versatile. As quantum technologies become prevalent, characterizing processing by system components will become increasingly important, and our technique is going to be applicable for quantum optical components in such systems.