This thesis presents the results of a series of four photonic experiments on the topic of quantum measurement. The first two experiments relate to quantum metrology, and the use of quantum states to increase the precision of measurements beyond what is possible with classical systems; first to detect and characterize decoherence, and then in the context of quantum imaging. The third experiment studies a fundamental question in quantum mechanics: "How much must a quantum system be disturbed by a measurement?". We use weak measurement to confirm a recent theoretical result, showing that if a particle's state is already sufficiently uncertain we can perform a measurement with very little disturbance -- contrary to common explanations of Heisenberg's uncertainty principle. The fourth experiment falls in the category of quantum computation. In quantum mechanics having multiple copies of an identical system allows us to extract more information than we can extract from a single copy (since quantum mechanics allows each system to be measured only once before collapsing). We present and experimentally implement a quantum algorithm to compress all of the "extractable information" present in an ensemble of identical copies of quantum bits into exponentially fewer quantum bits. The research presented here samples from a variety of topics in quantum information, showing in several contexts how fascinating quantum effects can be exploited to gain a "quantum enhancement".To enable these experiments two sources of entangled photons were built, and "hybrid" quantum systems (encoding information in multiple degrees of freedom of a photon) were used to implement quantum circuits. This thesis will present the details of one of these sources (a novel and practical source of entangled N00N states), which was used in a four-photon quantum metrology experiment. The other, more standard, source of polarization-entangled photon pairs will only briefly be reviewed to leave room for the discussion of hybrid quantum logic.
This thesis presents the results of a series of four photonic experiments on the topic of quantum measurement. The first two experiments relate to quantum metrology, and the use of quantum states to increase the precision of measurements beyond what is possible with classical systems; first to detect and characterize decoherence, and then in the context of quantum imaging. The third experiment studies a fundamental question in quantum mechanics: "How much must a quantum system be disturbed by a measurement?". We use weak measurement to confirm a recent theoretical result, showing that if a particle's state is already sufficiently uncertain we can perform a measurement with very little disturbance -- contrary to common explanations of Heisenberg's uncertainty principle. The fourth experiment falls in the category of quantum computation. In quantum mechanics having multiple copies of an identical system allows us to extract more information than we can extract from a single copy (since quantum mechanics allows each system to be measured only once before collapsing). We present and experimentally implement a quantum algorithm to compress all of the "extractable information" present in an ensemble of identical copies of quantum bits into exponentially fewer quantum bits. The research presented here samples from a variety of topics in quantum information, showing in several contexts how fascinating quantum effects can be exploited to gain a "quantum enhancement".To enable these experiments two sources of entangled photons were built, and "hybrid" quantum systems (encoding information in multiple degrees of freedom of a photon) were used to implement quantum circuits. This thesis will present the details of one of these sources (a novel and practical source of entangled N00N states), which was used in a four-photon quantum metrology experiment. The other, more standard, source of polarization-entangled photon pairs will only briefly be reviewed to leave room for the discussion of hybrid quantum logic.
Quantum metrology is a subfield of quantum information science that seeks to enhance measurement precision by exploiting quantum phenomena. This thesis presents three experimental investigations that are related to quantum metrology.The first experiment demonstrates a quantum-inspired sub-Rayleigh parameter estimation technique capable of resolving the separation and relative intensities of two incoherent light sources, positioned closer than the Rayleigh criterion. The method relies solely on passive linear optical components, making it readily implementable in standard optical laboratories without specialized equipment. The second experiment demonstrates a scalable protocol for compressing the quantum Fisher information of an arbitrarily large ensemble of identical quantum states into a single quantum state. As a proof of concept, we implement its simplest building block by compressing the quantum Fisher information contained in two qubits into a single qubit. The third experiment demonstrates that entangled probes can optimally estimate the strength of a dephasing channel, including the case where the dephasing axis is unknown.Together, these experiments provide examples of the capabilities of quantum metrology and offer new implementation ideas.
Quantum computation - the use of quantum systems as bits, or qubits, to perform computation - has been proven to be exponentially faster than what is thought possible with classical computation for several tasks. Quantum computers have the unique ability to store an amount of information that is exponential in the number of constituent particles used to encode that information. This property, which is arguably where quantum computers derive their power, makes it very difficult to characterize quantum systems. In order to fully characterize an unknown quantum state, a series of measurements must be performed on it and the state deduced from the results of those measurements. This process, called quantum tomography, is known to require exponential resources in the number of qubits. Both the number of measurements - the measurement complexity - and the number of times each measurement must be repeated - the sample complexity - present serious challenges when performing tomography. In addition, the measurement apparatus itself, which is usually a quantum system, must be characterized leading to even more experimental complexity. Here, I present three experiments which aim to reduce the experimental complexity of quantum tomography. The first aims to reduce the number of measurements needed to locate the decoherence-free subspaces of a noisy quantum channel. The process of locating these subspaces, which would normally require full process tomography, is performed with quadratically fewer measurement settings. The second experiment aims to characterize both an uncalibrated measurement apparatus and an unknown quantum state at the same time. With a specific model of measurement, it is found that an uncalibrated parameter of the measurement can be directly extracted using a single measurement. In the third experiment, I perform an experiment in which the optimal sample complexity for quantum state tomography is obtained using adaptivity: the ability to change measurement settings part way through an experiment. All three experiments were performed using the polarization degree of freedom of photons generated by spontaneous parametric downconversion. The source of photon pairs and the measurement techniques used are described in detail, along with the theory of quantum distinguishability and its relevance to tomography.
In this thesis, I present experimental and theoretical work which assesses and develops a range of tools that are required for performing quantum information processing, particularly in photonic systems. I investigate the three degrees of freedom of a single photon—its polarisation, spatialmomentum and time-frequency distributions. For polarisation, I show that using wave plates to implement arbitrary, single-qubit rotations is more complicated than is commonly appreciated. In the spatial-momentum and time-frequency domains, I develop ways to perform tomographic analysis of quantum states, and I report the first demonstrations of these techniques. In the time-frequency domain, the tomography technique utilises entanglement in the photon polarisation as a resource to store and provide access to the time-frequency information. In my first two experiments, I use spontaneous parametric down-conversion to produce entanglement between pairs of single photons in all three degrees of freedom. I demonstrate the first characterisation of entanglement in spatial modes and the time-frequency domain, the first quantitative measurement of entangled qutrit states, and the highest quality entangled states yet measured in both polarisation and spatial modes. I also report the first realisation of complete hyperentanglement, and a full, black-box tomography of a 36-dimensional two-photon state—the largest system to be characterised in this way to date. In my final experiment, I model and implement a new architecture for a controlled-Z gate which is much simpler to align than previous implementations. This gate requires only one non-classical interference condition, the visibility of which is the main limitation to its performance. I show that the gate operates effectively as a means of both creating entanglement and discriminating between the four elements in a basis of maximally entangled, Bell-type states. Indeed, its observed performance as a Bell analyser would be sufficient to build a quantum state teleporter which would guarantee that the recipient would be left with a better copy of an unknown input state than any eavesdropper. In a series of numerical simulations, I investigate some of the practicalities that arise when using tomographic reconstruction techniques, including how to estimate errors, which measurements to make and what is actually the optimal reconstruction. In particular, I show that tomographies perform better when based on the results from over-complete sets of measurements. Finally, I discuss the important issue of how to compare two processes, particularly when trying to assess the quality of a measured process by comparing it to some expected ideal. Judging possible candidate measures against a set of experimentally and theoretically motivated
Quantum technologies harness the properties of controlled quantum mechanical systems for applications in computation, communication and metrology, and enable us to further our understanding of fundamental physics. Quantum hardware is designed to manipulate complex and fragile many-particle quantum states, which requires exquisite control machinery, advanced software and near-complete isolation from the surrounding environment. With sufficient capabilities, quantum computers with large registers of quantum bits will perform classically intractable calculations such as quantum chemistry simulations. Quantum key distribution will provide completely secure communications across the world and quantum metrology will enable measurement precision beyond today's capabilities. While quantum technologies are far from surpassing classical hardware today, the vision and potential impact has sparked a world-wide research effort, both theoretical and experimental, to develop a quantum computer. The most sophisticated current quantum technologies have control over small numbers of quantum bits and are limited by environmental decoherence processes. While progress in developing quantum hardware is ongoing, designing and demonstrating new algorithms and protocols for quantum information is a thriving research field. Photonics provides an ideal platform for small-scale proof-of-concept quantum experiments, which are the focus of this thesis. In the coming decades, we will see the realisation of quantum hardware capable of applications that outperform any classical computer. In this thesis, I present several protocols and algorithms for quantum information science and technology, which are implemented in quantum photonic experiments. The applications of these works include robust quantum tomography, quantum state relocation, quantum enhanced data recovery and probing fundamental causality in quantum mechanics. The works presented here are based on two photon experiments from a prototypical spontaneous parametric down-conversion source, which provides an excellent test-bed for quantum information experiments. Photons can be used to encode quantum information in a range of different degrees of freedom. This versatility, along with compatibility with existing technology gives photonics a great advantage in the development of quantum hardware.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
The photon is a quantum system that is by nature robust against noise, and fast travelling, providing an ideal information carrier for quantum information science. The field of quantum information science has generated a great deal of interest for both researchers and the public due to the advantages it can have over classical technologies in areas including communication, computing and cryptography. In this thesis, I explore several different ways that photons can be used to realize quantum information advantages and enable quantum technologies, information tasks and fundamental studies of physics. A strong emphasis is placed on their practical implementation in optical experiments, where the challenges of noise, loss and device imperfections must be considered and combated. I utilize spontaneous parametric downconversion-based sources of high-quality single photons, and their polarization, path, and temporal degrees of freedom for encoding quantum information. In my first experimental project, I demonstrate the first violation of noncontextuality with time-polarization intraparticle entangled states encoded in a single photon by implementing a powerful interference-based measurement technique for photonic states. I perform a test of noncontextuality, acquiring a parameter |SCHSH| = 2.744 ± 0.006, which violates the classical bound of 2 by over 110 standard deviations, rigorously certifying both entanglement and contextuality of the system. We propose a new approach for preparing and measuring high-dimensional time-bin states, that overcomes many of the limitations of previous techniques, and demonstrate it for time-bin qubits and qutrits. In the next experimental project, I investigate the topic of universal cloning in quantum steering-with cloning and steering being two fundamental aspects of quantum physics deeply involved in the security of quantum protocols. I report the first experimental demonstration of cloned quantum steering, showing a simultaneous violation in a steering test by two clones made from one part of an entangled pair of photons. This provides a conclusive result on the question of whether the cloning of quantum steering is possible. We also present theoretical results that clarify our understanding of cloned steering for qubits: we find a no-go theorem where quantum steering can only be copied by a qubit universal cloning machine for 2 and 3 clones, and a monogamy relation where for N clones, steering is only possible if a minimum of N + 1 measurements are performed on each clone. I discuss the field of random number generation, and study how quantum physics allows for certifiably unpredictable random sequences, without needing complete trust in all of the physical devices, offering high levels of security over classical approaches. I report the first discrete-variable detection-loophole-free implementation of one-sided device-independent randomness expansion of certified random bits, based on the quantum steering task. These results illustrate an approach to secure randomness with greater tolerance to noise and loss compared to Bell test-based protocols. The final experimental project looks at quantum autoencoders, which are a quantum machine learning tool that we investigate for the purpose of denoising quantum states. I model and simulate a denoising quantum autoencoder which compresses ququarts into a qubit space and reconstructs noise-reduced ququart states. I construct an experimental apparatus that implements this device, and demonstrate quantum state tomography of ququart states, and the training of the autoencoder.