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.

/pdf/linear-optical-quantum-computing-with-photonic-qubits-9g7i3xmt3s.pdf

Linear optical quantum computing with photonic qubits

We report the creation of thermal, Fock, coherent, and squeezed states of motion of a harmonically bound {sup 9}Be{sup +} ion. The last three states are coherently prepared from an ion which has been initially laser cooled to the zero point of motion. The ion is trapped in the regime where the coupling between its motional and internal states, due to applied (classical) radiation, can be described by a Jaynes-Cummings-type interaction. With this coupling, the evolution of the internal atomic state provides a signature of the number state distribution of the motion. {copyright} {ital 1996 The American Physical Society.}

Generation of Non-classical Motional States of a Trapped Atom

The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These "quantum cloning machines" are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional and for continuous-variable quantum systems); in addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning.

Quantum cloning

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged d...

Effective Hamiltonian theory and its applications in quantum information

In this paper, we describe a general optomechanical system for converting photons to phonons in an efficient and reversible manner. We analyze classically and quantum mechanically the conversion process and proceed to a more concrete description of a phonon–photon translator (PPT) formed from coupled photonic and phononic crystal planar circuits. The application of the PPT to RF-microwave photonics and circuit QED, including proposals utilizing this system for optical wavelength conversion, long-lived quantum memory and state transfer from optical to superconducting qubits, is considered.

https://iopscience.iop.org/article/10.1088/1367-2630/13/1/013017/pdf

Proposal for an optomechanical traveling wave phonon–photon translator

We present a scheme to produce an entangled four-photon W state by using linear optical elements. The symmetrical setup of linear optical elements consists of four beam splitters, four polarization beam splitters, and four mirrors. A photon Einstein-Podolsky-Rosen pair and two single photons are required as the input modes. The projection on the W state can be made by a four-photon coincidence measurement. Further, we show that by means of a horizontally oriented polarizer in front of one detector, the W state of three photons can be generated.

https://arxiv.org/pdf/quant-ph/0202090.pdf

Generation of an entangled four-photon W state

We present a scheme to generate a maximally entangled state of two three-level atoms with a nonresonant cavity by cavity-assisted collisions. Since the cavity field is only virtually excited, no quantum information will be transferred from the atoms to the cavity.

https://arxiv.org/pdf/quant-ph/0303015.pdf

Generation of an entangled state of two three-level atoms in cavity QED

We propose a scheme to generate a four-particle Greenberger-Horne-Zeilinger (GHZ) state of distant atoms that are trapped separately in leaky cavities. This scheme uses cavity decay to inject photons into a setup of optical devices that consist of a symmetric series of beam splitters and photon detectors. Photon detection on the output modes of the beam splitters projects the atom-cavity-system state onto the GHZ state. It is briefly pointed out that this scheme can be extended to generate GHZ states of 4m atoms.

Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay

We propose a scheme to implement the $\stackrel{\ensuremath{\rightarrow}}{1}2$ universal quantum cloning machine of Buzek and Hillery [Phys. Rev. A $54,$ 1844 (1996)] in the context of cavity QED. The scheme requires cavity-assisted collision processes between atoms, which cross through nonresonant cavity fields in the vacuum states. The cavity fields are only virtually excited to face the decoherence problem. That's why the requirements on the cavity quality factor can be loosened.

Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED

We propose a unified scheme to generate W states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the W states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.

K. Pahlke

Papers

Generation of an entangled four-photon W state

Generation of an entangled state of two three-level atoms in cavity QED

Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay

Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED

Quantum entanglement of four distant atoms trapped in different optical cavities