Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

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Linear optical quantum computing with photonic qubits

Monodisperse colloidal suspensions of micrometre-sized spheres are playing an increasingly important role as model systems to study, in real space, a variety of phenomena in condensed matter physics—such as glass transitions and crystal nucleation1,2,3,4. But to date, no quantitative real-space studies have been performed on crystal melting, or have investigated systems with long-range repulsive potentials. Here we demonstrate a charge- and sterically stabilized colloidal suspension—poly(methyl methacrylate) spheres in a mixture of cycloheptyl (or cyclohexyl) bromide and decalin—where both the repulsive range and the anisotropy of the interparticle interaction potential can be controlled. This combination of two independent tuning parameters gives rise to a rich phase behaviour, with several unusual colloidal (liquid) crystalline phases, which we explore in real space by confocal microscopy. The softness of the interaction is tuned in this colloidal suspension by varying the solvent salt concentration; the anisotropic (dipolar) contribution to the interaction potential can be independently controlled with an external electric field ranging from a small perturbation to the point where it completely determines the phase behaviour. We also demonstrate that the electric field can be used as a pseudo-thermodynamic temperature switch to enable real-space studies of melting transitions. We expect studies of this colloidal model system to contribute to our understanding of, for example, electro- and magneto-rheological fluids.

A colloidal model system with an interaction tunable from hard sphere to soft and dipolar

The concept of the photon, central to Einstein's explanation of the photoelectric effect, is exactly 100 years old. Yet, while photons have been detected individually for more than 50 years, devices producing individual photons on demand have only appeared in the last few years. New concepts for single-photon sources, or 'photon guns', have originated from recent progress in the optical detection, characterization and manipulation of single quantum objects. Single emitters usually deliver photons one at a time. This so-called antibunching of emitted photons can arise from various mechanisms, but ensures that the probability of obtaining two or more photons at the same time remains negligible. We briefly recall basic concepts in quantum optics and discuss potential applications of single-photon states to optical processing of quantum information: cryptography, computing and communication. A photon gun's properties are significantly improved by coupling it to a resonant cavity mode, either in the Purcell or strong-coupling regimes. We briefly recall early production of single photons with atomic beams, and the operation principles of macroscopic parametric sources, which are used in an overwhelming majority of quantum-optical experiments. We then review the photophysical and spectroscopic properties and compare the advantages and weaknesses of various single nanometre-scale objects used as single-photon sources: atoms or ions in the gas phase and, in condensed matter, organic molecules, defect centres, semiconductor nanocrystals and heterostructures. As new generations of sources are developed, coupling to cavities and nano-fabrication techniques lead to improved characteristics, delivery rates and spectral ranges. Judging from the brisk pace of recent progress, we expect single photons to soon proceed from demonstrations to applications and to bring with them the first practical uses of quantum information.

https://iopscience.iop.org/article/10.1088/0034-4885/68/5/R04/pdf

Single-photon sources

This review covers state-of-the-art quantum teleportation technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms and solid-state systems. Open issues and potential future implementations are also discussed. Quantum teleportation is one of the most important protocols in quantum information. By exploiting the physical resource of entanglement, quantum teleportation serves as a key primitive across a variety of quantum information tasks and represents an important building block for quantum technologies, with a pivotal role in the continuing progress of quantum communication, quantum computing and quantum networks. Here we summarize the basic theoretical ideas behind quantum teleportation and its variant protocols. We focus on the main experiments, together with the technical advantages and disadvantages associated with the use of the various technologies, from photonic qubits and optical modes to atomic ensembles, trapped atoms and solid-state systems. After analysing the current state-of-the-art, we finish by discussing open issues, challenges and potential future implementations.

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Advances in quantum teleportation

Light harvesting components of photosynthetic organisms are complex, coupled,
many-body quantum systems, in which electronic coherence has recently been
shown to survive for relatively long time scales despite the decohering effects
of their environments. Within this context, we analyze entanglement in
multi-chromophoric light harvesting complexes, and establish methods for
quantification of entanglement by presenting necessary and sufficient
conditions for entanglement and by deriving a measure of global entanglement.
These methods are then applied to the Fenna-Matthews-Olson (FMO) protein to
extract the initial state and temperature dependencies of entanglement. We show
that while FMO in natural conditions largely contains bipartite entanglement
between dimerized chromophores, a small amount of long-range and multipartite
entanglement exists even at physiological temperatures. This constitutes the
first rigorous quantification of entanglement in a biological system. Finally,
we discuss the practical utilization of entanglement in densely packed
molecular aggregates such as light harvesting complexes.

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Quantum entanglement in photosynthetic light-harvesting complexes

We report the experimental realization of teleporting a one-particle entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one-photon state. Our experiment follows the line suggested by Lee and Kim [Phys. Rev. A 63, 012305 (2000)] and Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)]. An unprecedented large value of the teleportation ``fidelity'' has been attained: $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(95.3\ifmmode\pm\else\textpm\fi{}0.6)%$.

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Teleportation of a Vacuum–One-Photon Qubit

We report the experimental realization of the "active" quantum teleportation (QST) of a one-particle entangled qubit. This demonstration completes the original QST protocol and renders it available for actual implementation in quantum computation networks. It is accomplished by implementing a 8m optical delay line and a single-photon triggered fast Electro-Optic Pockels cell. A large value of teleportation "delity" was attained: Fa =( 90 2)%. Our work follows the line recently suggested by H. W. Lee and J. Kim, Phys. Rev. A 63, 012305 (2000) and E.Knill, R.Laflamme and G.Milburn Nature 409: 46 (2001). PACS: 03.65.Ud, 03.67.Hk, 42.50.Ar, 89.70.+c Quantum state teleportation (QST), introduced by C. H. Bennett, G.Brassard, C. Crepeau, R. Jozsa, A. Peres and W. Wootters came to be recognized in the last decade as a fundamental method of quantum communication and, more generally as one of the basic ideas of the whole eld of quantum information [1]. Following the original teleportation paper and its continuous-variables version [2] an intensive experimental eort started for the practical realization of teleportation. Quantum state teleportation (QST) was in facts realized in a number of experiments [3], [4] and [5]. Very recently a "qubit teleportation" with a unprecedented large "delity" (F 0:95) has been experimentally demonstrated by our laboratory in the context of quantum optics by adoption of the concept of "entanglement of one photon with the vacuum" by which each quantum superposition state, i.e. a qubit was physically implemented by a two dimensional subspace of Fock states of a mode of the electromagnetic eld, specically the space spanned by the QED "vacuum" and the 1-photon state [6]. Precisely, if A and B represent two dierent modes of the eld, with wavevectors (wv) kA and kB directed respectively towards two distant stations (Alice and Bob), these ones may be linked by a non-local channel expressed by an entangled state implying the quantum superposition of a single photon, e.g. by the singlet: ji singlet = 2 12 (j1i A j0i B j 0i A j1i B ). Here the mode indexes 0 and 1 denote respectively the vacuum and 1-photon Fock state population of the modes kA ;k B and the superposition state may be simply provided by an optical beam splitter (BS), as we shall see. The relevant conceptual novelty introduced here consists of the

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"Active" Teleportation of a Quantum Bit

We report the experimental realization of a recently discovered quantum-information protocol by Peres implying an apparent nonlocal quantum mechanical retrodiction effect. The demonstration is carried out by a quantum optical method by which each singlet entangled state is physically implemented by a two-dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the vacuum and the one-photon state, along lines suggested recently by E. Knill et al. [Nature (London) 409, 46 (2001)] and by M. Duan et al. [ibid. 414, 413 (2001)].

Delayed-choice entanglement swapping with vacuum–one-photon quantum states

We report the experimental realization of the “active” quantum teleportation (QST) of a one-particle entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one photon state. This demonstration completes the original QST protocol and renders it available for actual implementation in quantum computation networks. It is accomplished by implementing a 8 m optical delay line and a single-photon triggered fast Electro-Optic Pockels cell. A large value of teleportation “fidelity” was attained: Fa = 90 ∓ 2)%. Furthermore we present a scheme for delayed-entanglement swapping by applying the same quantum optical method.

Active teleportation and entanglement swapping of a vacuum-one photon qubit

We report the experimental realization of teleporting an entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one photon state. Our experiment follows along lines suggested by H. W. Lee and J. Kim, Phys. Rev. A, 63, 012305 (2000) and E.Knill, R.Laflamme and G.Milburn Nature 409: 46 (2001).

Egilberto Lombardi

Papers

Teleportation of a Vacuum–One-Photon Qubit

"Active" Teleportation of a Quantum Bit

Delayed-choice entanglement swapping with vacuum–one-photon quantum states

Active teleportation and entanglement swapping of a vacuum-one photon qubit

Teleportation of Entangled States of a Vacuum-One Photon Qubit