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AIP conference proceedings

Quantum-optical process tomography using coherent states

Mirko Lobino, Saleh Rahimi-Keshari, Dmitry Korystov, Connor Kupchak, Eden V. Figueroa, Artur Scherer, Barry C. Sanders, Alexander I. Lvovsky, Timothy C. Ralph, Ping Koy Lam

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We review the method for characterizing, with arbitrarily high accuracy, any quantum optical process, which our group has developed over the past few years. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We present a simple scheme for calculating the process matrix from this information. We demonstrate the capability of our protocol by demonstrating complete characterization of an optical memory based on electromagnetically induced transparency.

DOI
10.1063/1.3630179

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We review the method for characterizing, with arbitrarily high accuracy, any quantum optical process, which our group has developed over the past few years. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We present a simple scheme for calculating the process matrix from this information. We demonstrate the capability of our protocol by demonstrating complete characterization of an optical memory based on electromagnetically induced transparency.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, i.e. classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a method for characterizing, with arbitrarily high accuracy, any quantum optical process. Our protocol recovers complete knowledge of the process by studying, via homodyne tomography, its effect on a set of coherent states, that is, classical fields produced by common laser sources. We demonstrate the capability of our protocol by evaluating and experimentally verifying the effect of a test process on squeezed vacuum.
This thesis introduces and implements a characterization procedure called coherent state quantum process tomography and applies it to a selection of quantum operations. The procedure holds advantages over previous quantum process tomography methods, a pri- mary one is that a process can be characterized by measuring its effect on a set of coherent states which are readily available from a laser source. After introduction of the characterization procedure, the method is tested on a simple process of an electro-optical modulator and polarizing beam splitter. The accuracy of the characterization is verified by comparison of the predicted action of the reconstructed process tensor versus the actual experiment involving a squeezed vacuum state. The algorithm is then implemented and verified on a quantum memory system based on electromagnetically induced transparency, a system that was previously shown capable of storing a squeezed vacuum state. Lastly, a new optical storage system based on a gradient echo memory scheme is con- structed and optimized to achieve memory retrieval efficiencies of >80%. To characterize this system, a modified coherent state quantum process tomography algorithm based on the method of maximum likelihood estimation is employed. Despite the high efficiency values, the presence of excess noise resulted in the degradation of the storage device per- formance to be below the benchmarks of a quantum memory system. This estimation algorithm is also successfully implemented on the non-deterministic processes of photon creation and annihilation.
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally feasible set of coherent states and its related energy-cutoff approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a few different coherent states without approximations like the energy cutoff. For tomography of multimode processes, our method exponentially reduces the number of different test states, compared with existing methods.
We report a technique for experimental characterization of an M -mode quantum optical process, generalizing the single-mode coherent-state quantum-process tomography method [ 1 , 2 ]. By measuring the effect of the process on multi-mode coherent states via balanced homodyne tomography, we obtain the process tensor in the Fock basis. This rank- tensor, which predicts the effect of the process on an arbitrary density matrix, is iteratively reconstructed directly from the experimental data via the maximum-likelihood method. We demonstrate the capabilities of our method using the example of a beam splitter, reconstructing its process tensor within the subspace spanned by the first three Fock states. In spite of using purely classical probe states, we recover quantum properties of this optical element, in particular the Hong–Ou–Mandel effect.
We report complete characterization of an optical memory based on electromagnetically induced transparency. We recover the superoperator associated with the memory, under two different working conditions, by means of a quantum process tomography technique that involves storage of coherent states and their characterization upon retrieval. In this way, we can predict the quantum state retrieved from the memory for any input, for example, the squeezed vacuum or the Fock state. We employ the acquired superoperator to verify the nonclassicality benchmark for the storage of a Gaussian distributed set of coherent states.