The Gaussian toolbox of the continuous variables provides for deterministic, high-efficiency operations with non-classical states. Its very Gaussian nature, however, restricts its reach for quantum information and communication applications. This thesis comprises three experimental works, which seek to examine the strengths of this toolbox and address some of its weaknesses. The measurement-based non-linearity of a conditional photon-counting measurement can be used to de-Gaussify' a Gaussian state of light. Here, we propose a continuous variable analog of just such a 'heralding' measurement, replacing a non-deterministic photon-counting measurement with a deterministic measurement of the field quadratures. Such a technique cannot be used to prepare a non-Gaussian state, but it can, on average, yield the same non-Gaussian statistics. We demonstrate this technique by reconstructing the statistics of non-Gaussian photon-subtracted squeezed vacuum states. We then consider the problem of noiseless linear amplification. We experimentally demonstrate that in certain scenarios, the requirement for a physical noiseless linear amplifier can be exchanged for a straightforward post-selection of the measurement record. We apply our 'virtual' noiseless amplifier to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We extract an effective entangled resource stronger than even that achievable with a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of the value of the measurement-based noiseless linear amplifier for quantum key distribution, extracting a secret key from an otherwise insecure regime. Lastly, we turn to the recently popularised measure of all quantum correlations: quantum discord. Quantum discord has emerged as a measure of quantum correlations beyond entanglement, with significant ramifications for our understanding of Gaussian states. Here, we introduce a simple protocol that yields an operational interpretation of quantum discord: that discord describes information only accessible via coherent interactions. We first experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interactions is directly linked to the discord of the original state.
The Gaussian toolbox of the continuous variables provides for deterministic, high-efficiency operations with non-classical states. Its very Gaussian nature, however, restricts its reach for quantum information and communication applications. This thesis comprises three experimental works, which seek to examine the strengths of this toolbox and address some of its weaknesses. The measurement-based non-linearity of a conditional photon-counting measurement can be used to de-Gaussify' a Gaussian state of light. Here, we propose a continuous variable analog of just such a 'heralding' measurement, replacing a non-deterministic photon-counting measurement with a deterministic measurement of the field quadratures. Such a technique cannot be used to prepare a non-Gaussian state, but it can, on average, yield the same non-Gaussian statistics. We demonstrate this technique by reconstructing the statistics of non-Gaussian photon-subtracted squeezed vacuum states. We then consider the problem of noiseless linear amplification. We experimentally demonstrate that in certain scenarios, the requirement for a physical noiseless linear amplifier can be exchanged for a straightforward post-selection of the measurement record. We apply our 'virtual' noiseless amplifier to entanglement degraded by transmission loss of up to the equivalent of 100km of optical fibre. We extract an effective entangled resource stronger than even that achievable with a maximally entangled resource passively transmitted through the same channel. We also provide a proof-of-principle demonstration of the value of the measurement-based noiseless linear amplifier for quantum key distribution, extracting a secret key from an otherwise insecure regime. Lastly, we turn to the recently popularised measure of all quantum correlations: quantum discord. Quantum discord has emerged as a measure of quantum correlations beyond entanglement, with significant ramifications for our understanding of Gaussian states. Here, we introduce a simple protocol that yields an operational interpretation of quantum discord: that discord describes information only accessible via coherent interactions. We first experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interactions is directly linked to the discord of the original state.
In this thesis we consider quantum communication as realised in the continuous variable quantum optical regime. The work presented includes results concerning quantum communication applications, such as entanglement distillation and quantum key distributions, as well as fundamental questions regarding measurement uncertainty and the boundary between classical and quantum correlations. In the first part of the thesis we investigate various protocols in which one engages in a trade-off between determinism and the quality of quantum correlations. In discrete variable quantum optics non-determinism is ubiquitous, with photon sources, detectors and various gates commonly operating probabilistically. In the continuous variable regime one has access to many quantum states and operations, including exotic effects such as entanglement, in a fully deterministic fashion and one might regard giving up this feature as highly undesirable. However it has been discovered that certain vital tasks such as entanglement distillation, indispensable for large scale quantum information networks, cannot be realised deterministically. We address precisely these limitations, firstly by conducting the most general analysis to date of a non-deterministic but heralded quantum amplifier that can circumvent the standard quantum limits, and distill Gaussian entanglement. We then analyse the security of long standing technique in continuous variable quantum key distribution, known as post-selection, which again allows the distillation of higher quality correlations. We provide a complete security proof in the asymptotic limit and show that there is in fact an relationship between this method and the noiseless amplifier. Furthermore, the protocol allows secure key to be generated for channel parameters where all previous CVQKD protocols fail. Thirdly we consider this equivalence between post-selection and heralded operations more generally, and conduct a detailed analysis of the post-selection based emulation of the noiseless amplifier. Turning to more fundamental issues, we consider links between several recently proposed entropic measures of quantum correlations and their potential operational links to continuous variable quantum key distribution. Finally we consider entropic uncertainty relations for continuous variables on infinite dimensional Hilbert spaces and apply these to one-sided device independent continuous variable quantum key distribution protocols.n
This thesis presents results under the topics of quantum correlations and quantum information processing using linear-optical networks. The first part of this thesis concerns with quantum correlations, specially in Gaussian states, which play a central role as resource in quantum protocols. The second part is about quantum information processing using linear-optical networks that are of great practical interest due to their simple physical realization. In the first part, we present a measurement-based method for verifying nonzero quantum discord, a measure of quantum correlations, in bipartite systems that can be used for both continuous and discrete-variable systems. Based on this method, we show that the only bipartite Gaussian states with zero quantum discord are product states. We also present a simple and efficient experimental method for verifying quantum correlations in Gaussian states using homodyne measurements. Moreover, we introduce an operational measure for quantifying quantum correlations in Gaussian states that is purely based on Gaussian measurements. We then illustrate the operational significance of the measure in terms of a Gaussian quantum protocol. In the second part, we present results on linear quantum-optics experiments, specifically boson sampling, an intermediate model of quantum computation that can be implemented using single-photon states, linear-optical networks, and photodetectors. We first present an efficient experimental method for characterization of linear-optical networks, which is essential for practical implementation of boson sampling. We show that using coherent states one can directly measure all the nontrivial phases and moduli of the matrix describing the network. Next, we consider the problem of boson sampling with Gaussian states. We derive a general formula for calculating the output photon-counting probabilities. We show that for input thermal states, sampling from the output probability distribution can be efficiently classically simulated. Using this, we find that permanents of positive-semidefinite Hermitian matrices can be approximated to within a multiplicative error in BPPNP. We also discuss boson sampling with squeezed vacuum states. Finally, we provide a sufficient condition for the efficient classical simulation of the general sampling problem using linear-quantum optics, which involves a multimode input quantum state to a linear-optical network and set of measurements at the output. This condition is based on the phase-space quasiprobability distributions, and suggests that negativity is a quantum resource. We apply this condition to implementations of boson sampling using single-photon or spontaneous parametric down-conversion sources. We show that above some threshold for loss and noise in the experiment, boson sampling is classically simulatable.
Quantum states can be correlated in ways beyond what is possible for classical states. These correlations are considered as the main resource for quantum computation and communication tasks. In this thesis, I present my studies on the different forms of Quantum Correlations known as "Quantum Discord", "Einstein-Podolsky-Rosen(EPR) Steering" and "Bel-type correlations" in the continuous-variable quantum states and investigate their practical applications for the secure quantum communication. While previously quantum entanglement was considered as the only form of quantum correlation, in the recent years a notion known as quantum discord which captures extra quantum correlations beyond entanglement was introduced by Ollivier and Zurek. This sort of non-classicality that can exist even in separable states, has raised so much aspiration for the potential applications, as they are less fragile than the entangled states. Therefore, of especial interest is to know if a bipartite quantum state is discordant or not. In this thesis I will describe the simple and efficient experimental technique that we have introduced and experimentally implemented to verify quantum discord in unknown Gaussian states and a certain class of non-Gaussian states. According to our method, the peak separation between the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurement conducted on the other subsystem is an indication of nonzero quantum discord. We implemented this method experimentally by preparing bipartite Gaussian and non-Gaussian states and proved nonzero quantum discord in all the prepared states. Though quantum key distribution has become a mature technology, the possibility of hacking the devices used in the quantum communications has motivated the scientists to develop the schemes where one or non of the devices used by the communicating parties need to be trusted. Quantum correlations are the key to develop these schemes. Particularly, EPR steering is connected to the one-sided-deviceindependent quantum key distribution in which devices of one party are solely trusted and Bell-type correlations to the fully device-independent quantum key distribution where non of the apparatuses of the communicating parties is trusted. Here, I will present the result of our theoretical and experimental research to develop one-sided-device-independent quantum key distribution in continuous variables. We identify all Gaussian protocols that can in principle be one-sided-device independent. This consists of 6 protocols out of 16 possible Gaussian protocols, which surprisingly includes the protocol that applies only coherent states. We experimentally implemented both the entanglement-based and coherent state protocols and manifested their loss tolerance. Our results open the door for the practical secure quantum communications, asserting the link between the EPR-steering andone-sided-device-independence. Due to the maturity of quantum information using continuous variables, it is important to develop a Bell-type inequality in this regime. Despite its fundamental importance, Bell-type correlation is linked to the device-independent quantum key distribution. I developed a computer modelling based on the proposal of ref [1, 2] to demonstrate continuous-variable Bell-type correlation. The results of my computer simulations that are presented in this thesis show the feasibility of these proposals, which makes the real-life implementation of continuous-variable device-independent quantum key distribution possible.
We introduce a simple and efficient technique to verify quantum discord in unknown Gaussian states and certain class of non-Gaussian states. We show that any separation in the peaks of the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurements performed on the other subsystem indicates correlation between the corresponding quadratures and hence nonzero quantum discord. We also demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interaction.
The characterisation of quantum correlations, also known as entanglement, is central to quantum information theory. Operationally, entanglement gives rise to the notion of quantum non-locality, which challenges the ‘reality’ of quantum mechanics (adopting the terminology of Einstein, Podolski and Rosen) and arguably represents its most distinctive feature, in the sense that it calls for a departure from certain foundational tenets of classical physics. It should thus not come as a surprise that entanglement turns out to be a key resource for the implementation of a number of quantum communication protocols and also necessary to achieve computational speed-ups with quantum hardware, in the sense that accessing regions of the Hilbert space with entangled states allows one to shorten the computational depth of certain algorithms. Not surprisingly, generating and maintaining entanglement is generally difficult in practice, as it requires strong interactions between selected components of a system that must at the same time be isolated from the environment. Thanks to the techniques developed in quantum optical set-ups to achieve squeezed light, entanglement is, however, comparatively accessible with optical quantum continuous variables. As we shall see, in fact, continuous variable entanglement is closely related to the notion of squeezing. It is therefore of the utmost importance to be able to qualify and quantify the entanglement of quantum continuous variables, which is the subject matter of the present chapter. The first part of the chapter is devoted to techniques and criteria based on second moments to detect the entanglement of Gaussian states and also to the description of possible ways to quantify such quantum correlations, bearing in mind that the determination of entanglement monotones of clear operational significance is still an open problem, even in the restricted arena of Gaussian states. Although the criteria based on second moments are sufficient, but not necessary, for the detection of non-Gaussian entanglement too, we will push our analysis further by introducing more general criteria based on higher order statistical moments, which will be put to use to detect, on paper, the quantum correlations of an entangled cat-like state. We will also address the issues of entanglement distillation and quantum non-locality tests, in whose contexts we shall encounter other non-Gaussian operations and states, such as photon-subtracted states.
Quantum communication and computation harness the intriguing and bewildering nature of quantum mechanics to realize information processing tasks that have no classical analog. Nonetheless, this supremacy comes with fundamental limits that, in some scenarios, pose undesirable bounds on the performance of these quantum technologies. One such example is the well-known quantum no-cloning theorem imposed by the Heisenberg uncertainty principle. It states that an unknown quantum state cannot be duplicated with arbitrarily high accuracy. Very recently, however, post-selection was proposed as a way out: it was demonstrated that in various quantum information tasks, deterministic bounds can be overcome by forgoing determinism. In this thesis, we investigate post-selection as a novel approach to enhance the performance of versatile continuous-variable (CV) quantum information processing and envisage it to become a useful component of the general Gaussian toolbox. The first part of this thesis examines applications of post-selection in purely linear systems. In particular, two implementations of the noiseless linear amplifier (NLA), the measurement-based NLA and the physical NLA, are investigated and compared in terms to their abilities to preserve the state Gaussianity and their success probability. We show that the inevitable signal-to-noise ratio (SNR) degradation accompanying a linear quantum amplifier can be circumvented by resorting to a probabilistic scheme. Amplification with a signal transfer coefficient of Ts>1 is realised by combining a measurement-based NLA with a deterministic linear amplifier. We also construct a quantum cloning machine based on this hybrid amplifier for arbitrary coherent input states. We demonstrate a production of multiple clones (up to five) with fidelity of each clone exceeding the corresponding no-cloning limit. We then consider employing the post-selection algorithm in information protocols involving nonlinearity. First, we develop two squeezers as optical parametric amplifiers, each producing fairly pure squeezed output field up to 11.2dB (after correcting the detection loss). The squeezers are served as the nonlinear source in the remaining part of this thesis. We demonstrate a high fidelity quantum squeezing gate which is one indispensible building block for constructing a universal CV quantum computer. An inverse-Gaussian filter is incorporated into the feedforward line, leading to an enhancement in precision of the inline dual-homodyne measurement and therefore combats efficiently the correlation degradation due to loss and noise introduced during feedforward. As one example, we show that a fidelity of 98.49% for a target squeezing of -2.3dB is obtained with only -6dB ancilla squeezing, which would otherwise require -20.5dB initial squeezing using a conventional deterministic setup. Additionally, we introduce a CV quantum teleportation scheme using post-selection, allowing for a significantly improved fidelity against the conventional deterministic CV teleporter. The intuition behind this improvement is that post-selection effectively distilled the accessible entanglement and therefore a high fidelity only originally achievable with a higher amount of initial squeezing is now obtainable with only modest amount of squeezing, coming at an expense of finite success probability.