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.
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.
In the past decade, quantum communication protocols based on continuous variables (CV) has seen considerable development in both theoretical and experimental aspects. Nonetheless, challenges remain in both the practical security and the operating range for CV systems, before such systems may be used extensively. In this thesis, we present the optimisation of experimental parameters for secure randomness generation and propose a non-deterministic approach to enhance amplification of CV quantum state. The first part of this thesis examines the security of quantum devices: in particular, we investigate quantum random number generators (QRNG) and quantum key distribution (QKD) schemes. In a realistic scenario, the output of a quantum random number generator is inevitably tainted by classical technical noise, which potentially compromises the security of such a device. To safeguard against this, we propose and experimentally demonstrate an approach that produces side-information independent randomness. We present a method for maximising such randomness contained in a number sequence generated from a given quantum-to-classical-noise ratio. The detected photocurrent in our experiment is shown to have a real-time random-number generation rate of 14 (Mbit/s)/MHz. Next, we study the one-sided device-independent (1sDI) quantum key distribution scheme in the context of continuous variables. By exploiting recently proven entropic uncertainty relations, one may bound the information leaked to an eavesdropper. We use such a bound to further derive the secret key rate, that depends only upon the conditional Shannon entropies accessible to Alice and Bob, the two honest communicating parties. We identify and experimentally demonstrate such a protocol, using only coherent states as the resource. We measure the correlations necessary for 1sDI key distribution up to an applied loss equivalent to 3.5 km of fibre transmission. The second part of this thesis concerns the improvement in the transmission of a quantum state. We study two approximate implementations of a probabilistic noiseless linear amplifier (NLA): a physical implementation that truncates the working space of the NLA or a measurement-based implementation that realises the truncation by a bounded postselection filter. We do this by conducting a full analysis on the measurement-based NLA (MB-NLA), making explicit the relationship between its various operating parameters, such as amplification gain and the cut-off of operating domain. We compare it with its physical counterpart in terms of the Husimi Q-distribution and their probability of success. We took our investigations further by combining a probabilistic NLA with an ideal deterministic linear amplifier (DLA). In particular, we show that when NLA gain is strictly lesser than the DLA gain, this combination can be realised by integrating an MB-NLA in an optical DLA setup. This results in a hybrid device which we refer to as the heralded hybrid quantum amplifier. A quantum cloning machine based on this hybrid amplifier is constructed through an amplify-then-split method. We perform probabilistic cloning of arbitrary coherent states, and demonstrate the production of up to five clones, with the fidelity of each clone clearly exceeding the corresponding no-cloning limit.
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
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 processing of information based on the generation of common quantum optical states (e.g. coherent states) and the measurement of the quadrature components of the light field (e.g. homodyne detection) is often referred to as continuous-variable quantum information processing. It is a very fertile field of investigation, at a crossroads between quantum optics and information theory, with notable successes such as unconditional continuous-variable quantum teleportation or Gaussian quantum key distribution. In quantum optics, the states of the light field are conveniently characterized using a phase-space representation (e.g. Wigner function), and the common optical components effect simple affine transformations in phase space (e.g. rotations). In quantum information theory, one often needs to determine entropic characteristics of quantum states and operations, since the von Neuman entropy is the quantity at the heart of entanglement measures or channel capacities. Computing entropies of quantum optical states requires instead turning to a state-space representation of the light field, which formally is the Fock space of a bosonic mode. This interplay between phase-space and state-space representations does not represent a particular problem as long as Gaussian states (e.g. coherent, squeezed, or thermal states) and Gaussian operations (e.g. beam splitters or squeezers) are concerned. Indeed, Gaussian states are fully characterized by the first- and second-order moments of mode operators, while Gaussian operations are defined via their actions on these moments. The so-called symplectic formalism can be used to treat all Gaussian transformations on Gaussian states, including mixed states of an arbitrary number of modes, and the entropies of Gaussian states are directly linked to their symplectic eigenvalues. This thesis is concerned with the Gaussian transformations applied onto arbitrary states of light, in which case the symplectic formalism is unapplicable and this phase-to-state space interplay becomes highly non trivial. A first motivation to consider arbitrary (non-Gaussian) states of light results from various Gaussian no-go theorems in continuous-variable quantum information theory. For instance, universal quantum computing, quantum entanglement concentration, or quantum error correction are known to be impossible when restricted to the Gaussian realm. A second motivation comes from the fact that several fundamental quantities, such as the entanglement of formation of a Gaussian state or the communication capacity of a Gaussian channel, rely on an optimization over all states, including non-Gaussian states even though the considered state or channel is Gaussian. This thesis is therefore devoted to developing new tools in order to compute state-space properties (e.g. entropies) of transformations defined in phase-space or conversely to computing phase-space properties (e.g. mean-field amplitudes) of transformations defined in state space. Remarkably, even some basic questions such as the entanglement generation of optical squeezers or beam splitters were unsolved, which gave us a nice work-bench to investigate this interplay. In the first part of this thesis (Chapter 3), we considered a recently discovered Gaussian probabilistic transformation called the noiseless optical amplifier. More specifically, this is a process enabling the amplification of a quantum state without introducing noise. As it has long been known, when amplifing a quantum signal, the arising of noise is inevitable due to the unitary evolution that governs quantum mechanics. It was recently realized, however, that one can drop the unitarity of the amplification procedure and trade it for a noiseless, albeit probabilistic (heralded) transformation. The fact that the transformation is probabilistic is mathematically reflected in the fact that it is non trace-preserving. This quantum device has gained much interest during the last years because it can be used to compensate losses in a quantum channel, for entanglement distillation, probabilistic quantum cloning, or quantum error correction. Several experimental demonstrations of this device have already been carried out. Our contribution to this topic has been to derive the action of this device on squeezed states and to prove that it acts quite surprisingly as a universal (phase-insensitive) optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time. This also brought into surface a paradoxical effect, namely that such a device could seemingly lead to instantaneous signaling by circumventing the quantum no-cloning theorem. This paradox was discussed and resolved in our work. In a second step, the action of the noiseless optical amplifier and it dual operation (i.e. heralded noiseless attenuator) on non-Gaussian states has been examined. We have observed that the mean-field amplitude may decrease in the process of noiseless amplification (or may increase in the process of noiseless attenuation), a very counterintuitive effect that Gaussian states cannot exhibit. This work illustrates the above-mentioned phase-to-state space interplay since these devices are defined as simple filtering operations in state space but inferring their action on phase-space quantities such as the mean-field amplitude is not straightforward. It also illustrates the difficulty of dealing with non-Gaussian states in Gaussian transformations (these noiseless devices are probabilistic but Gaussian). Furthermore, we have exhibited an experimental proposal that could be used to test this counterintuitive feature. The proposed set-up is feasible with current technology and robust against usual inefficiencies that occur in optical experiment. Noiseless amplification and attenuation represent new important tools, which may offer interesting perspectives in quantum optical communications. Therefore, further understanding of these transformations is both of fundamental interest and important for the development and analysis of protocols exploiting these tools. Our work provides a better understanding of these transformations and reveals that the intuition based on ordinary (deterministic phase-insensitive) amplifiers and losses is not always applicable to the noiseless amplifiers and attenuators. In the last part of this thesis, we have considered the entropic characterization of some of the most fundamental Gaussian transformations in quantum optics, namely a beam splitter and two-mode squeezer. A beam splitter effects a simple rotation in phase space, while a two-mode squeezer produces a Bogoliubov transformation. Thus, there is a well-known phase-space characterization in terms of symplectic transformations, but the difficulty originates from that one must return to state space in order to access quantum entropies or entanglement. This is again a hard problem, linked to the above-mentioned interplay in the reverse direction this time. As soon as non-Gaussian states are concerned, there is no way of calculating the entropy produced by such Gaussian transformations. We have investigated two novel tools in order to treat non-Gaussian states under Gaussian transformations, namely majorization theory and the replica method. In Chapter 4, we have started by analyzing the entanglement generated by a beam splitter that is fed with a photon-number state, and have shown that the entanglement monotones can be neatly combined with majorization theory in this context. Majorization theory provides a preorder relation between bipartite pure quantum states, and gives a necessary and sufficient condition for the existence of a deterministic LOCC (local operations and classical communication) transformation from one state to another. We have shown that the state resulting from n photons impinging on a beam splitter majorizes the corresponding state with any larger photon number n’ > n, implying that the entanglement monotonically grows with n, as expected. In contrast, we have proven that such a seemingly simple optical component may have a rather surprising behavior when it comes to majorization theory: it does not necessarily lead to states that obey a majorization relation if one varies the transmittance (moving towards a balanced beam splitter). These results are significant for entanglement manipulation, giving rise in particular to a catalysis effect. Moving forward, in Chapter 5, we took the step of introducing the replica method in quantum optics, with the goal of achieving an entropic characterization of general Gaussian operations on a bosonic quantum field. The replica method, a tool borrowed from statistical physics, can also be used to calculate the von Neumann entropy and is the last line of defense when the usual definition is not practical, which is often the case in quantum optics since the definition involves calculating the eigenvalues of some (infinite-dimensional) density matrix. With this method, the entropy produced by a two-mode squeezer (or parametric optical amplifier) with non-trivial input states has been studied. As an application, we have determined the entropy generated by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple, yet unknown analytical expression. Finally, we have turned to the replica method in the context of field theory, and have examined the behavior of a bosonic field with finite temperature when the temperature decreases. To this end, information theoretical tools were used, such as the geometric entropy and the mutual information, and interesting connection between phase transitions and informational quantities were found. More specifically, dividing the field in two spatial regions and calculating the mutual information between these two regions, it turns out that the mutual information is non-differentiable exactly at the critic
Abstract We propose a method to improve transmission distance of continuous-variable quantum key distribution via a heralded hybrid linear amplifier (HLA), involving an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The phase-insensitive amplification of quantum light states may experience a degradation of signal-to-noise ratio (SNR) of 3dB which can be surmounted by the probabilistic amplification process. The new hybrid amplifier allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. Our equipment could clone unknown coherent states with fidelity surpassing the no-cloning limit by abandoning determinism and using probabilistic methods. The setup has a better compatibility with continuous variable protocols as it only uses Gaussian elements and a post-selection algorithm. The hybrid linear amplifier enhances the SNR and hence the transmission distance of the CVQKD protocol is extended. Both the asymptotic secret key rate and the secret key rate in a finite-size scenario are analyzed in this paper.
Nonlocal quantum gates, coupling quantum systems located at a distance, are crucial for distributed quantum computing. To this aim, high-capacity optical noiseless connections between different processing units are essential for transmitting large amounts of information per mode. Simultaneously, optical quantum computing offers future high-speed multimode quantum processors. We propose a library of feasible protocols to implement a necessary nonlocal continuous-variable (CV) quantum nondemolition (QND) gate between two distant users sharing a quantum channel and exploiting classical communication. The users are endowed with a newly achieved high-fidelity and large-bandwith element - single-pass phase-sensitive optical parametric amplifier (OPA), that allows for both online squeezing and channel-loss compensation. The use of OPAs enhances quality of the resulting gate in terms of both excess noise and entangling capability. The proposed schemes are also applicable to CV cluster state fusion, providing a first step towards development of distributed CV measurement-based quantum computation.