On experimental procedures for entanglement verification

We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in infering entanglement when there is none. We distinguish protocols meant to refute or eliminate hidden-variable models from those meant to verify entanglement.Comment: 15 page

The Quantum State of an Ideal Propagating Laser Field

We give a quantum information-theoretic description of an ideal propagating CW laser field and reinterpret typical quantum-optical experiments in light of this. In particular we show that contrary to recent claims [T. Rudolph and B. C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be used for quantum teleportation with continuous variables and for generating continuous-variable entanglement. Optical coherence is not required, but phase coherence is. We also show that coherent states play a priveleged role in the description of laser light.Comment: 4 pages RevTeX, to appear in PRL. For an extended version see quant-ph/011115

Strongly focused light beams interacting with single atoms in free space

We construct 3-D solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.Comment: 9 pages, 9 figure

Two roles of relativistic spin operators

Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into "spin" and "orbital" parts reveals the difference between these two roles. We also discuss a relation of different choices of spin observables to the violation of Bell inequalities.Comment: RevTeX 4, 4 pages A discussion on relation of different choices of spin observables to the observed violation of Bell inequalities is added, some misprints corrected and the presentation is clarifie

Decoherence of multi-dimensional entangled coherent states

For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multi-dimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order $2^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equal to $2/\log(2)\approx 2.89$ ebits per absorbed photon, irrespective of the amount of pure-state entanglement $E$ one started with. In contrast, for larger losses it tends to be the remaining amount of entanglement that is independent of $E$. This may provide a useful strategy for creating states with a fixed amount of entanglement.Comment: 6 pages, 5 figure

The Effect of Stochastic Noise on Quantum State Transfer

We consider the effect of classical stochastic noise on control laser pulses used in a scheme for transferring quantum information between atoms, or quantum dots, in separate optical cavities via an optical connection between cavities. We develop a master equation for the dynamics of the system subject to stochastic errors in the laser pulses, and use this to evaluate the sensitivity of the transfer process to stochastic pulse shape errors for a number of different pulse shapes. We show that under certain conditions, the sensitivity of the transfer to the noise depends on the pulse shape, and develop a method for determining a pulse shape that is minimally sensitive to specific errors.Comment: 10 pages, 9 figures, to appear in Physical Review

Entanglement and purity of single- and two-photon states

Whereas single- and two-photon wave packets are usually treated as pure states, in practice they will be mixed. We study how entanglement created with mixed photon wave packets is degraded. We find in particular that the entanglement of a delocalized single-photon state of the electro-magnetic field is determined simply by its purity. We also discuss entanglement for two-photon mixed states, as well as the influence of a vacuum component.Comment: 11 pages, 10 figures, 1 debuting autho

Unambiguous State Discrimination of Coherent States with Linear Optics: Application to Quantum Cryptography

We discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurements is shown to be optimal in the limit of small photon numbers for any N. For the special case of N=4 this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the BB84 quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, if he detects two photons Bob will unambiguously know the bit sent to him in 50% of the cases without having to exchange basis information, and if three photons are detected, Bob will know unambiguously which quantum state was sent.Comment: 5 RevTeX pages, 2 eps figure

Error free quantum communication through noisy channels

We suggest a method to perform a quantum logic gate between distant qubits by off-resonant field-atom dispersive interactions. The scheme we present is shown to work ideally even in the presence of errors in the photon channels used for communication. The stability against errors arises from the paradoxical situation that the transmitted photons carry no information about the state of the qubits. In contrast to a previous proposal for ideal communication [Phys. Rev. Lett. 78, 4293 (1997)] our proposal only involves single atoms in the sending and receiving devices.Comment: 6 pages, including 2 figure