The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
This chapter presents the basic concepts necessary to use photons as physical implementations of qubits. It starts with a traditional field quantization approach in the optical domain, where it puts an emphasis on how to obtain field modes which can be used as single localizable qubits. After quickly touching on several ways of generating single photon states, it moves to more technical aspects of parametric down conversion, which up to now has been the workhorse for most of the demonstration experiments involving two or a few more qubits in entangled states of high purity. The reader should be able to understand most aspects of contemporary sources of this type. The chapter then finishes by touching upon a few qubit operations with photons, exploring the high temporal correlation of down converted photon pairs, which also allow for at least a partial Bell state analysis.
Quantum communication attempts to harness the unique rules of quantum mechanics to perform communication tasks that are difficult or impossible using classical rules. To realize these benefits, information must be carried on quantum systems. Photons make excellent carriers because they interact very little with the environment, move quickly, and can naturally store quantum information in their polarization. However, it is notoriously difficult to detect a single photon without destroying it. Standard detectors simply absorb the photon, losing the quantum information. This is a critical outstanding problem in quantum communication, as advanced protocols need to know exactly when a photon has arrived at a receiver after transmission through the atmosphere or an optical fibre before performing further quantum-information-processing tasks. Certifying a photon’s presence is of particular interest in tests of Bell’s inequalities, which have only recently been performed without loopholes arising from photon loss, and in device-independent quantum cryptography, which relies on such Bell tests for security. \n \nIn this thesis, I first present work on directly reducing losses in a successful loophole-free Bell test. This is an extremely difficult task that cannot be extended for long-distance communication. Therefore I then focus on ways to circumvent loss by detecting photons without destroying them while preserving their quantum information. First I analyze theoretically a way to herald photons using only linear-optical elements (beam splitters and phase shifters) and extra ancilla photons. Similar but older methods have been demonstrated experimentally by other groups, and my improvements will help future advanced quantum communication protocols. \n \nThe main experiment in this thesis certifies the presence of a photon in a rather simple way: split the photon into two using a nonlinear optical crystal, then detect one of the pair to herald the other. I show in this first proof-of-principle experiment that photonic qubit precertification indeed preserves qubit states, with up to (92.3 ± 0.6)% fidelity and rates of 1100 events per hour. With reductions in detector dark counts, precertification could outperform direct transmission, even with extremely lossy fibre links. \n \nFinally, I present two sources of photons based on nonlinearities in optical fibres. One of the limitations of the photon splitting scheme for heralding is the low success probability due to the very low likelihood of splitting a photon in two. In these fibre photon sources I investigate increasing the splitting likelihood in four-wave mixing through advanced materials and fibre designs. I use polarization-maintaining fibres to generate entangled photon pairs as a prerequisite to precertification, with (92.2 ± 0.2)% fidelity to a maximally-entangled state. Then I show that one type of highly nonlinear chalcogenide glass, never before used for photon pair generation, could outperform standard nonlinear crystals by two orders of magnitude, with calculated conversion efficiency up to 10^-3. To approach the single photon regime, I generate photon pairs in chalcogenide microwires with pump powers as low as 480 nW and verify their timing correlations. \n \nThese advances demonstrate the capability of nondestructive precertification of photons to allow advanced quantum communications protocols even over long distance, and could lead to the first implementations of fully device-independent quantum cryptography.
Quantum information processing opens up completely new possibilities in communication and computation, that would be impossible in the realms of classical physics. While the benefits of quantum information processing are well understood in theory, it remains a formidable challenge to experimentally implement even simple quantum information processing tasks. Numerous physical architectures have been proposed for preparing and coherently manipulating quantum information. Amongst these, quantum optics has been identified as a particularly promising candidate. In particular this arises from the long decoherence times of single photon states, which can be used to encode logical qubits in a variety of ways. Nonetheless, there remain formidable challenges to implementing large scale quantum information processing using optical qubits. Most notably these include: the preparation of pure indistinguishable photons; efficient number-resolving photo-detection; mode-matching; photon loss; and the non-determinism of entangling gates. Any future large scale implementation of optical quantum information processing protocols will require significant advances on most, if not all these fronts. In this thesis we aim to present a comprehensive overview of the major requirements for optical quantum information processing, understand the effects they have, and how they can be modeled. From this we aim to understand what the realistic technological requirements are to achieve scalable optical quantum information processing, and, where possible, suggest means by which to help achieve these goals.
We present two types of photon sources designed for secure quantum communication, e.g. for quantum cryptography. Both types are based on the creation of photon pairs by spontaneous parametric downconversion in nonlinear crystals. The first is a heralded single photon source and the second is a source of polarization-entangled photon pairs. For the heralded single photon source the detection of one of the photons of a downconversion pair is used as a trigger to announce the presence of the other: the single photon. The source is characterized by a highly sub-Poisson photon number statistics making it very suitable for use in quantum cryptography protocols using single photonic qubits to create correlated information between a sender and a receiver. The entanglement source instead uses the inherent non-classical correlations between entangled qubits. We also present a hybrid-encoding where the sender uses polarization to encode information while the receiver uses time-bins. Both sources create photons with highly non-degenerate wavelengths of 810 nm and 1550 nm, taking advantage of the efficient detectors at near-infrared and the low transmission loss of optical fibers at telecommunication wavelengths.
Compared with other physical platforms for Quantum Information Processing (QIP), photons have the unique advantages of travelling over free-space links or optical fiber with relatively low decoherence and of propagating with minimal coupling to the environment, while also being easily coupled to existing telecommunications technology. The R&D of various single photon and entangled photon generation technologies and the linear-optical implementations of quantum computation and communication are now surveyed and analyzed in a structured manner. We discuss photonic qubit degrees of freedom (polarization, time-bin, path, frequency and Orbital angular momentum), determine sources such as deterministic quantum-dot based sources and probabilistic sources based on spontaneous parametric down conversion (SPDC), and review architectures for Linear Optical Quantum Computation (LOQC), such as the Knill–Laflamme–Milburn (KLM) protocol and measurement-based quantum computation. Building on the density-matrix treatment of biexciton–exciton coherent dynamics in semiconductor quantum dots, we recapitulate the development of two-pulse coherent control schemes for generation and readout of photonic qubits in these systems and how they have been stretched towards optical control of logic gates. A comparative performance framework is established along the lines of source brightness, entanglement fidelity, photon indistinguishability, channel loss and scalability, which is illustrated by simulated performance plots and tabulated against literature numbers. Remaining hurdles in the field regarding issues of photon loss, scalable multiplexing, deterministic two-qubit interaction, and its integration with a quantum memory are highlighted and a perspective is provided on hybrid photonic–matter architectures for fault-tolerant quantum networks.
In the previous chapter we developed some of the basic aspects of quantum information processing with single photons as qubits. Apart from noting the obvious benefit of using light for quantum communication, we identified some difficulties in manipulating quantum information that is encoded in photons. In particular, it is difficult to construct two-qubit gates for photonic qubits. In this chapter we will have to face this difficulty head-on in our discussion of quantum computation with single photons and linear-optical elements. The possibility of a quantum computer based on single photons, linear optics, and photon counting was demonstrated in a landmark paper by Knill, Laflamme, and Milburn in 2001. Their protocol is commonly referred to as the ‘ klm protocol’. In subsequent years, the klm protocol has been dramatically slimmed down in terms of complexity and the necessary resources to create the universal set of quantum gates. For pedagogical reasons we give the streamlined version here, and we briefly describe the original klm protocol in Appendix 2. We will make extensive use of the results in Section 1.4 about mode transformations, and Section 2.3 about cluster-state quantum computing. We start this chapter, however, with a description of linear-optical networks, and how they fail as deterministic quantum computers. In Section 6.2 we discuss the principle of post-selection, and how this can be used to create probabilistic gates with deterministic feed-forward control.