Entanglement of internal and external angular momenta of a single atom

We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre-Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic center-of-mass motion is quantized. The spin and orbital angular momenta of the field are individually conserved upon absorption, and this results in the entanglement of the internal and external degrees of freedom of the atom. We suggest applications of this entanglement in quantum information processing.Comment: 4 pages, 2 figure

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

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

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

Classical Rules in Quantum Games

We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.Comment: The previous title, "Quantum games are no fun (yet)", was too whimsical for Physical Review. This is a comment on most, but not all, papers on quantum game theor

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

Verifying entanglement in the Hong-Ou-Mandel dip

The Hong-Ou-Mandel interference dip is caused by an entangled state, a delocalized bi-photon state. We propose a method of detecting this entanglement by utilizing inverse Hong-Ou-Mandel interference, while taking into account vacuum and multi-photon contaminations, phase noise, and other imperfections. The method uses just linear optics and photodetectors, and for single-mode photodetectors we find a lower bound on the amount of entanglement.Comment: 5 pages, 2 figure

The phosphate balance : current developments and future outlook

Phosphate is essential for agricultural production and therefore plays a key role in the global production of food and biofuels. There are no agricultural alternatives for phosphate, and a substantial fraction of our annual phosphate consumption is dispersed into the environment where it is largely lost to agriculture. Phosphate is an irreplaceable, and to a considerable extent non-renewable, resource that is being exploited at an ever increasing rate. The ongoing depletion of phosphate resources combined with recently increased phosphate prices urge us to reconsider our phosphate consumption patterns. In addition to economic and geo-political reasons, further reducing phosphate consumption would moreover be beneficial to the quality of our environment. Even if we increase the reserve base, for which there are plenty of opportunities, it is clear that the phosphate industry will sooner or later have to make a switch from a reserve-based industry to a recycling industry

Reference frames, superselection rules, and quantum information

Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etcetera. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This article reviews the role of reference frames and superselection rules in the theory of quantum information processing.Comment: 55 pages, published versio