A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal

Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizing both of the above examples. The dual protocols responsible for this decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf'' protocol (FQSW), a generalization of the recently discovered ``quantum state merging'', is related to FF by source-channel duality, and to FQRS by time reversal duality, thus forming a triangle of dualities. The source-channel duality is identified as the origin of the previously poorly understood ``mother-father'' duality. Due to a symmetry breaking, the dualities extend only partially to classical information theory.Comment: 5 pages, 5 figure

Vacuum state truncation via the quantum Zeno effect

In the context of quantum state engineering we analyze the effect of observation on nonlinear optical $n$-photon Fock state generation. We show that it is possible to truncate the vacuum component from an arbitrary photon number superposition without modifying its remaining parts. In the course of the full dynamical analysis of the effect of observation, it is also found that the Zeno and the anti-Zeno effects repeat periodically. We discuss the close relationship between vacuum state truncation and so-called "interaction-free" measurement.Comment: 4 pages, 2 figures, LaTeX; TeX errors fixe

Stabilisation of Quantum Computations by Symmetrisation

We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into $\cal SYM$, the symmetric subspace of the full state space of $R$ redundant copies of the computer. We describe an efficient algorithm and quantum network effecting $\cal SYM$--projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.Comment: 20 pages LaTeX, 2 postscript figure

Distinguishability of States and von Neumann Entropy

Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with prior probabilities p_j respectively. We show that it is possible to increase all of the pairwise overlaps || i.e. make each constituent pair of the states more parallel (while keeping the prior probabilities the same), in such a way that the von Neumann entropy S is increased, and dually, make all pairs more orthogonal while decreasing S. We show that this phenomenon cannot occur for ensembles in two dimensions but that it is a feature of almost all ensembles of three states in three dimensions. It is known that the von Neumann entropy characterises the classical and quantum information capacities of the ensemble and we argue that information capacity in turn, is a manifestation of the distinguishability of the signal states. Hence our result shows that the notion of distinguishability within an ensemble is a global property that cannot be reduced to considering distinguishability of each constituent pair of states.Comment: 18 pages, Latex, 2 figure

On quantum coding for ensembles of mixed states

We consider the problem of optimal asymptotically faithful compression for ensembles of mixed quantum states. Although the optimal rate is unknown, we prove upper and lower bounds and describe a series of illustrative examples of compression of mixed states. We also discuss a classical analogue of the problem.Comment: 23 pages, LaTe

Optical Communication Noise Rejection Using Correlated Photons

This paper describes a completely new way to perform noise rejection using a two-photon sensitive detector and taking advantage of the properties of correlated photons to improve an optical communications link in the presence of uncorrelated noise. In particular, a detailed analysis is made of the case where a classical link would be saturated by an intense background, such as when a satellite is in front of the sun,and identifies a regime where the quantum correlating system has superior performance.Comment: 12 pages, 1 figure, 1 tabl

Electronic spin drift in graphene field effect transistors

We studied the drift of electron spins under an applied DC electric field in single layer graphene spin valves in a field effect transport geometry at room temperature. In the metallic conduction regime ($n \simeq 3.5 \times 10^{16}$ m$^{-2}$), for DC fields of about $\pm$70 kV/m applied between the spin injector and spin detector, the spin valve signals are increased/decreased, depending on the direction of the DC field and the carrier type, by as much as $\pm$50%. Sign reversal of the drift effect is observed when switching from hole to electron conduction. In the vicinity of the Dirac neutrality point the drift effect is strongly suppressed. The experiments are in quantitative agreement with a drift-diffusion model of spin transport.Comment: 4 figure

Counterfactual Quantum Cryptography

Quantum cryptography allows one to distribute a secret key between two remote parties using the fundamental principles of quantum mechanics. The well-known established paradigm for the quantum key distribution relies on the actual transmission of signal particle through a quantum channel. This paper shows that the task of a secret key distribution can be accomplished even though a particle carrying secret information is not in fact transmitted through the quantum channel. The proposed protocols can be implemented with current technologies and provide practical security advantages by eliminating the possibility that an eavesdropper can directly access the entire quantum system of each signal particle.Comment: 19 pages, 1 figure; a little ambiguity in the version 1 removed; abstract, text, references, and appendix revised; suggestions and comments are highly appreciate

Quantum Key Distribution with Classical Bob

Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present a protocol with this constraint, and prove its robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe

Secure quantum key distribution with an uncharacterized source

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol for an arbitrary source whose averaged states are basis-independent, a condition that is automatically satisfied if the source is suitably designed. The proof is based on the observation that, to an adversary, the key extraction process is equivalent to a measurement in the sigma_x-basis performed on a pure sigma_z-basis eigenstate. The dependence of the achievable key length on the bit error rate is the same as that established by Shor and Preskill for a perfect source, indicating that the defects in the source are efficiently detected by the protocol.Comment: 4 pages, 1 figure, REVTeX, minor revision