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Journal of Experimental and Theoretical Physics Letters

Tomography of Optical Single-Qubit Quantum Memory

B. I. Bantysh, Konstantin G. Katamadze, Yu. I. Bogdanov, K. I. Gerasimov, Mansur M. Minnegaliev, R. V. Urmancheev, Sergey A. Moiseev

Published Jul 1, 2022• 5 citations
Publisher

Abstract

Optical quantum memory is one of the basic elements of quantum information systems. However, the possibilities of its application in such systems sometimes can hardly be estimated by existing methods for its characterization. In this work, the tomography of quantum memory has been implemented as a quantum process in a logical basis. It has been shown that the implemented quantum memory scheme for polarization photon qubits with a high accuracy corresponds to the identity transformation and is promising for application in quantum communication and quantum computing.

DOI
10.1134/s0021364022600951

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Optical quantum memory is one of the basic elements of quantum information systems. However, the possibilities of its application in such systems sometimes can hardly be estimated by existing methods for its characterization. In this work, the tomography of quantum memory has been implemented as a quantum process in a logical basis. It has been shown that the implemented quantum memory scheme for polarization photon qubits with a high accuracy corresponds to the identity transformation and is promising for application in quantum communication and quantum computing.
Efficient application of optical qubits for quantum information processing is impossible without a robust technology of their characterization. To date, characterization of optical logical ensembles has been based on studying relative photon number statistics in each mode and in their various linear superpositions as well as (in the case of multiple qubits) photon number correlations between modes. This approach is based on postselection and does not provide a correct performance estimate of an experimental scheme under investigation, in particular, it does not allow one to evaluate its scalability.
Quantum state tomography (QST) estimates an unknown quantum state from a measurement process typically performed on identical copies of the target state and plays a core role in characterizing quantum information systems. However, because quantum measurement outcomes are probabilistic, QST methods often require many shots per basis to achieve high-fidelity estimates, which hinders scalability to many-qubit applications and slows the transmission of quantum information. A more efficient procedure is therefore required for modern-day quantum operations in quantum computing, communications, and sensing. We address this need with an adaptive QST approach that measures a single-qubit state in a wide set of bases. We include bases beyond the Pauli triad {X,Y,Z} by leveraging the infinite-dimensional Hilbert space of quantum mechanics, increasing the likelihood of producing highly polarized measurement outcomes and finding an optimally informative basis. With this basis, the state can be identified with fewer measurements by focusing on directions that most reduce uncertainty of the state. In addition to theoretical innovation in [9], we experimentally verify in a simplified photonic realization using 13 bases that having many more available measurement bases than the Pauli triad benefits QST. This engineering implementation demonstrates that adaptive QST is both efficient in performance and practical to implement.
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.
Quantum memory is a key element for quantum repeaters and linear optical quantum computers. In addition to memory, repeaters and computers also require manipulating quantum states by means of unitary transformations, which is generally accomplished using interferometric optical setups. We experimentally investigate photon-echo type atom-light interaction for the possibility to combine storage with controlled transformation of quantum states. As an example, we demonstrate unambiguous state discrimination of qubits and qutrits in an Ti:Er:LiNbO3_33​ waveguide cooled to 3K using states encoded into large ensembles of identically prepared photons in superposition of different temporal modes. The high robustness and flexibility of our approach makes it promising for quantum communication and computation as well as precision measurements.
Quantum storage of flying optical qubits, namely coherently mapping photonic states into and out of an optically controlled memory on demand, constitutes an essential component in the optical quantum information processing science, with applications to long-distance optical communication [1]. In this context, practical protocols require sufficiently large storage efficiency to achieve a performance better than direct transmission. Theoretically, the storage and retrieval efficiency can only be improved with the increase of the optical depth (OD). Recent progresses have shown that high OD media enable to reach high-efficiency electromagnetically induced transparency (EIT)-based optical storage, albeit without the demonstration of qubit storage [2, 3]. Here we experimentally implement an optical quantum memory with single-photon-level probes, showing a EIT-based storage efficiency around 70%. Furthermore, thanks to the spatial multiplexing of the dense atomic ensemble, highly efficient storage of polarization qubit is performed.
Optical photons are powerful carriers of quantum information, which can be delivered in free space by satellites or in fibers on the ground over long distances. Entanglement of quantum states over long distances can empower quantum computing, quantum communications, and quantum sensing. Quantum optical memories are devices designed to store quantum information in the form of stationary excitations, such as atomic coherence, and are capable of coherently mapping these excitations to flying qubits. Quantum memories can effectively store and manipulate quantum states, making them indispensable elements in future long-distance quantum networks. Over the past two decades, quantum optical memories with high fidelities, high efficiencies, long storage times, and promising multiplexing capabilities have been developed, especially at the single-photon level. In this review, we introduce the working principles of commonly used quantum memory protocols and summarize the recent advances in quantum memory demonstrations. We also offer a vision for future quantum optical memory devices that may enable entanglement distribution over long distances.