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arXiv:1803.05981 · Physical Review A

Entanglement enhancement in multimode integrated circuits

Zacharie M. Léger, Aharon Brodutch, Amr Saher Helmy

Published Jun 4, 2018• 3 citations
arXivHTMLPDF

Abstract

The faithful distribution of entanglement in continuous-variable systems is essential to many quantum information protocols. As such, entanglement distillation and enhancement schemes are a cornerstone of many applications. The photon subtraction scheme offers enhancement with a relatively simple setup and has been studied in various scenarios. Motivated by recent advances in integrated optics, particularly the ability to build stable multimode interferometers with squeezed input states, a multimodal extension to the enhancement via photon subtraction protocol is studied. States generated with multiple squeezed input states, rather than a single input source, are shown to be more sensitive to the enhancement protocol, leading to increased entanglement at the output. Numerical results show the gain in entanglement is not monotonic with the number of modes or the degree of squeezing in the additional modes. Consequently, the advantage due to having multiple squeezed input states can be maximized when the number of modes is still relatively small (e.g., four). The requirement for additional squeezing is within the current realm of implementation, making this scheme achievable with present technologies.

DOI
10.1103/physreva.97.062303

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The faithful distribution of entanglement in continuous-variable systems is essential to many quantum information protocols. As such, entanglement distillation and enhancement schemes are a cornerstone of many applications. The photon subtraction scheme offers enhancement with a relatively simple setup and has been studied in various scenarios. Motivated by recent advances in integrated optics, particularly the ability to build stable multimode interferometers with squeezed input states, a multimodal extension to the enhancement via photon subtraction protocol is studied. States generated with multiple squeezed input states, rather than a single input source, are shown to be more sensitive to the enhancement protocol, leading to increased entanglement at the output. Numerical results show the gain in entanglement is not monotonic with the number of modes or the degree of squeezing in the additional modes. Consequently, the advantage due to having multiple squeezed input states can be maximized when the number of modes is still relatively small (e.g., four). The requirement for additional squeezing is within the current realm of implementation, making this scheme achievable with present technologies.
Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.
The subtraction of a single photon from a multimode quantum field is analyzed as the conditional evolution of an open quantum system. We develop a theory describing different subtraction schemes in a unified approach and we introduce the concept of subtraction modes intrinsic to the process. The matching between the subtraction modes and the modes of the field defines different possible scenarios for the photon subtraction. In particular, our framework identifies: the conditions of pure photon subtraction, the quantum states of the field modes conditioned to the photon subtraction, the mode with the highest fidelity with a single-photon state when the subtraction is performed on multimode squeezed light. We use our theory to analyze the photon subtraction from a highly multimode quantum resource - a train of quantum squeezed or correlated optical pulses. Performing the photon subtraction optimally on various multimode light field has the potential to implement a number of quantum information protocols in a multiplexed and scalable way.
Photonics quantum networks are pivotal for quantum technologies, facilitating efficient information distribution and manipulation through quantum states of light. Continuous-variable (CV) cluster states, essential resources for Measurement-Based Quantum Computing, can be deterministically generated using squeezed states of light and mode-basis changes [1]. However, Gaussian states like squeezed states or cluster states, can be efficiently simulated with a classical computer [2]. Thus, to achieve quantum advantage, non-Gaussianity should be introduced, which can be accomplished by subtracting a photon from a squeezed state [3].
Single-photon-level non-Gaussian operations—photon addition, photon subtraction, and their coherent superposition—are powerful tools with which to increase entanglement in continuous-variable optical states. Although such operations are typically not deterministic, there may be other advantages such as noiseless manipulation. Therefore, to fully account for the efficacy of a particular non-Gaussian operation in a practical scenario, we develop figures of merit which trade off the advantages of such protocols against their success probability. Specifically, we define 'entanglement enhancement rate' as the increase in entanglement per trial of a generic non-Gaussian operation on a two-mode squeezed vacuum (TMSV) state. We consider states generated by photon-subtraction, photon-addition and a coherent superposition of subtraction and addition. We compare each strategy when applied to one or both modes of a TMSV state, and also in the presence of channel losses prior to the operation. In many cases, additional properties are analytically calculable, including excess noise arising from the operation and the fidelity of the resulting states to particular Gaussian and non-Gaussian states. Finally, by incorporating loss, we derive optimal interaction parameters for each non-Gaussian operation which maximize the effectiveness of the particular protocol under investigation.
The nature of a quantum network, in particular in the continuous variable regime, is governed not only by the light quantum state but also by the measurement process. It can then be chosen after the light source has been generated. Multimode entanglement is not anymore an intrinsic property of the source but a complex interplay between source, measurement and eventually post processing. This new avenue paves the way for adaptive and scalable quantum information processing. However, to reach this ambitious goal, multimode degaussification has to be implemented. Single-photon subtraction and addition have proved to be such key operations, but are usually performed with linear optics elements on single-mode resources. We present a device able to perform mode dependant non Gaussian operation on a spectrally multimode squeezed vacuum states. Sum frequency generation between the state and a bright control beam whose spectrum has been engineered through ultrafast pulse-shaping is performed. The detection of a single converted photon heralds the success of the operation. The resulting multimode quantum state is analysed with standard homodyne detection whose local oscillator spectrum is independently engineered. The device can be characterized through quantum process tomography using weak multimode coherent states as inputs. Its single-mode character can be quantified and its inherent subtraction modes can be measured. The ability to simultaneously control the state engineering and its detection ensures both flexibility and scalability in the production of highly entangled non-Gaussian quantum states.
Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk opticslike proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently available integrated bulk-optics analog: the array of nonlinear waveguides. We theoretically demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We exhibit this versatility through analytical and numerically optimized multimode squeezing, entanglement, and cluster-state generation in different encodings. Our results re-establish spatial encoding as a contender in the game of continuous-variable quantum information processing.