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Journal of Modern Optics

Engineering of optical continuous-variable qubits via displaced photon subtraction: multimode analysis

Masahiro Takeoka, Jonas Schou Neergaard-Nielsen, Makoto Takeuchi, Kentaro Wakui, Hiroki Takahashi, K. Hayasaka, Masahide Sasaki

Published Nov 25, 2010• 5 citations
Publisher

Abstract

We investigate the practical scheme of engineering a qubit of two optical continuous-variable states, based on squeezed vacuum and coherently displaced photon subtraction. A fully multimode model is developed to describe a continuous wave (cw) setting of the experiment, which has been successfully implemented to generate highly pure non-classical states. The model agrees well with the experimental results and the numerical results show that the intrinsic imperfection due to the cw nature of the source is relatively small. Our photon subtraction technique could also be useful for preparing optical Schrödinger's cat-like states in arbitrary superposition, which is a basic qubit resource for linear optics coherent state quantum computing.

DOI
10.1080/09500340.2010.533205

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We investigate the practical scheme of engineering a qubit of two optical continuous-variable states, based on squeezed vacuum and coherently displaced photon subtraction. A fully multimode model is developed to describe a continuous wave (cw) setting of the experiment, which has been successfully implemented to generate highly pure non-classical states. The model agrees well with the experimental results and the numerical results show that the intrinsic imperfection due to the cw nature of the source is relatively small. Our photon subtraction technique could also be useful for preparing optical Schrödinger's cat-like states in arbitrary superposition, which is a basic qubit resource for linear optics coherent state quantum computing.
In a new branch of quantum computing, information is encoded into coherent states, the primary carriers of optical communication. To exploit it, quantum bits of these coherent states are needed, but it is notoriously hard to make superpositions of such continuous-variable states. We have realized the complete engineering and characterization of a qubit of two optical continuous-variable states. Using squeezed vacuum as a resource and a special photon-subtraction technique, we could with high precision prepare an arbitrary superposition of squeezed vacuum and a squeezed single photon. This could lead the way to demonstrations of coherent state quantum computing.
A theoretical analysis is given for a two-photon subtraction from a continuous-wave squeezed vacuum with finite time separation between two detection events. In the cw photon subtraction process, generated states are inevitably described by temporal multimode states. Our approach is based on analytical formulas that are mathematically simple and provide an intuitive understanding of the multimode structure of the system. We show that, in our process, the photon-subtracted squeezed vacuum is generated in two temporal modes and one of these modes acts as an ancillary mode to make the other one a large-amplitude coherent-state superposition.
Continuous-variable quantum information processing through quantum optics offers a promising platform for building the next generation of scalable fault-tolerant information processors. To achieve quantum computational advantages and fault tolerance, non-Gaussian resources are essential. In this work, we propose and analyze a method to generate a variety of non-Gaussian states using coherent photon subtraction from a two-mode squeezed state followed by photon-number-resolving measurements. The proposed method offers a promising way to generate rotation-symmetric states conventionally used for quantum error correction with binomial codes and truncated Schrödinger cat codes. We consider the deleterious effects of experimental imperfections such as detection inefficiencies and losses in the state engineering protocol. Our method can be readily implemented with current quantum photonic technologies.
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 photon subtraction provides an experimentally feasible option to construct large non-Gaussian quantum states in continuous variable quantum optics. The non-Gaussian features of the state can lead towards the more exotic aspects of quantum theory, such as negativity of the Wigner function. However, the payoff for states with such delicate quantum properties is their sensitivity to decoherence. In this paper, we present a general model that treats the most important source of decoherence in a purely optical setting: losses. We use the framework of open quantum systems and master equations to describe losses in nnn-photon-subtracted multimode states, where each photon can be subtracted in an arbitrary mode. As a main result, we find that mode-dependent losses and photon subtraction generally do not commute. In particular, the losses do not only reduce the purity of the state, they also change the modal structure of its non-Gaussian features. We then conduct a detailed study of single-photon subtraction from a multimode Gaussian state, which is a setting that lies within the reach of present-day experiments.