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arXiv:1702.00200 · Quantum Measurements and Quantum Metrology

Heralded orthogonalisation of coherent states and their conversion to discrete-variable superpositions

Regina Kruse, Christine Silberhorn, Tim J. Bartley

Published Dec 20, 2017• 2 citations
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Abstract

Abstract The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. Here, we present an experimentally feasible protocol for the probabilistic orthogonalisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, a successful operation of our protocol is heralded without measuring the states. As such, they remain suitable for further manipulation and the obtained orthogonal states serve as a discretevariable basis. Therefore, our protocol doubles as a simple continuous-to-discrete variable converter, which may find application in hybrid continuous-discrete quantum information processing protocols.

DOI
10.1515/qmetro-2017-0005

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Abstract The nonorthogonality of coherent states is a fundamental property which prevents them from being perfectly and deterministically discriminated. Here, we present an experimentally feasible protocol for the probabilistic orthogonalisation of a pair of coherent states, independent of their amplitude and phase. In contrast to unambiguous state discrimination, a successful operation of our protocol is heralded without measuring the states. As such, they remain suitable for further manipulation and the obtained orthogonal states serve as a discretevariable basis. Therefore, our protocol doubles as a simple continuous-to-discrete variable converter, which may find application in hybrid continuous-discrete quantum information processing protocols.
The study of entanglement between discrete and continuous variables is an important theoretical and experimental topic in quantum information processing, for which entanglement swapping is one of the interesting elements. Entanglement swapping allows two particles without interacting with each other in any way, to form an entangled state by the action of another pair of entangled particles. In this paper, we propose an experimentally feasible scheme to realize deterministic entanglement swapping in the hybrid system with discrete and continuous variables. The process is achieved by preparing two pairs of entangled states, each is formed by a qubit and two quasi-orthogonal coherent state elements of a cavity, performing a Bell-state analysis through nonlocal operations on the continuous variable states of the two cavities, and projecting the two qubits into a maximally entangled state. The present scheme may be applied to other physical systems sustaining such hybrid discrete and continuous forms, providing a typical paradigm for entanglement manipulation through deterministic swapping operations.
A probabilistic method for the unambiguous modification of non-orthogonal quantum states is proposed. This is based on conclusive modifications of the inner product between two pure quantum states in a discrimination-like process. We experimentally implemented this protocol by using two-photon polarization states generated in the process of spontaneous parametric down conversion. In the experiment, for codifying initial quantum states, we consider single photon states and heralded detection. As application, we show that when our protocol is applied to partially entangled states it allows a fine control of the amount of entanglement of the modified states.
This thesis presents an investigation into the generation and characterisation of non-Gaussian states in continuous variable quantum optics. Beginning by placing the study of continuous variables within the context of quantum information processing more generally, we then motivate the need for non-Gaussianity within quantum computing protocols. The focus then narrows to the consideration of two particular sets of non-Gaussian states: orthogonal superposition states and the cubic resource state. The superposition of two orthogonal states has been shown to enhance certain continuous variable quantum information processing protocols that rely on entanglement, and within this section two distinct methods for generating such states are considered. While one of these methods provides a specific example, the other introduces a general orthogonaliser that relies solely on knowledge of the expectation value for the chosen orthogonalising operator in order to produce the superposition. The second case for non-Gaussian state generation employs current results demonstrating the production of a weak approximation of the cubic resource state in order to illustrate the use of such single-mode states to generate multimode states with similar features. These states are implemented as ancillas for a deterministic non-Gaussian gate operation on a system of choice. We show that generating multimode states through this distribution scheme allows an enhancement of the output state to better approximate the nonlinear features. Finally, we consider methods of characterising non-Gaussian states. In particular, we introduce a witness for pure states existing outside of the Gaussian convex hull. Such states exclude Gaussian pure states as well as non-Gaussian states generated from mixtures of squeezed and coherent states, and therefore consist of non-Gaussian states generated from non-Gaussian operations. We present a detection-independent bound for such states based on the generalised quasiprobability distribution.
In this paper we propose a probabilistic method which allows an unambiguous modification of two nonorthogonal quantum states. We experimentally implement this protocol by using two-photon polarization states generated in the process of spontaneous parametric down conversion. In the experiment, for codifying initial quantum states, we consider single-photon states and heralded detection. We show that the application of this protocol to entangled states allows a fine control of the amount of entanglement of the initial state.
Probabilistic heralded Gaussification of quantum states of light is an important ingredient of protocols for distillation of continuous variable entanglement and squeezing. An elementary step of the heralded Gaussification protocol consists of interference of two copies of the state at a balanced beam splitter, followed by conditioning on the outcome of a suitable Gaussian quantum measurement on one output mode. When iterated, the protocol either converges to a Gaussian state or diverges. Here, we report on experimental investigation of the convergence properties of iterative heralded Gaussification. We experimentally implement two iterations of the protocol, which requires simultaneous processing of four copies of the input state. We utilize the phase-randomized coherent states as the input states, which greatly facilitates the experiment because these states can be generated deterministically, and their mean photon number can easily be tuned. We comprehensively characterize the input and partially Gaussified states by balanced homodyne detection and quantum state tomography. Our experimental results are in good agreement with theoretical predictions and they provide new insights into the convergence properties of heralded quantum Gaussification.