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arXiv:1409.3719 · Nature Physics

Hybrid discrete- and continuous-variable quantum information

Ulrik L. Andersen, Jonas Schou Neergaard-Nielsen, Peter van Loock, Akira Furusawa

Published Sep 1, 2015• 441 citations
arXivHTMLPDF
DOI
10.1038/nphys3410

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Quantum teleportation, a transfer protocol of quantum states, is the essence of many sophisticated quantum information protocols. There have been two complementary approaches to optical quantum teleportation: discrete variables (DVs) and continuous variables (CVs). However, both approaches have pros and cons. Here we take a “hybrid” approach to overcome the current limitations: CV quantum teleportation of DVs. This approach enabled the first realization of deterministic quantum teleportation of photonic qubits without post-selection. We also applied the hybrid scheme to several experiments, including entanglement swapping between DVs and CVs, conditional CV teleportation of single photons, and CV teleportation of qutrits. We are now aiming at universal, scalable, and fault-tolerant quantum computing based on these hybrid technologies.
Abstract In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bell-cat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, refered as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, refered as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the two complementary encodings have emerged [1]. In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete and continuous-variable quantum states generated using optical parametric oscillators [2], located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Here we will report the first protocols based on this resource: the remote preparation of continuous-variable qubits [3], and a violation of an Einstein-Podolosky-Rosen steering inequality [4].
Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.