Marek Zukowski

Multiphoton entanglement and interferometry

Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gda´nski, 80-952 Gda ´nsk, PolandReceived 14 June 2002, accepted 21 June 2002Published online 30 April 2003Multiphoton entanglement is the basis of many quantum communication schemes, quantum cryptographicprotocols, and fundamental tests of quantum theory. Spontaneous parametric down-conversion is the mosteffective source for polarization entangled photon pairs. Here we show, that a class of entangled 4-photonstates can be directly created by parametric down-conversion. These states exhibit perfect quantum correla-tions and a high robustness of entanglement against photon loss. Therefore these states are well suited fornew types of quantum communication.

Bell's theorem for general N-qubit states.

We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.

Experimental interference of independent photons.

Interference of photons emerging from independent sources is essential for modern quantum-information processing schemes, above all quantum repeaters and linear-optics quantum computers. We report an observation of nonclassical interference of two single photons originating from two independent, separated sources, which were actively synchronized with a rms timing jitter of 260 fs. The resulting (two-photon) interference visibility was (83+/-4)%.

Experimental Observation of Four-Photon Entanglement from Parametric Down-Conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.

Bell’s Inequalities and Quantum Communication Complexity

We prove that for every Bell’s inequality and for a broad class of protocols, there always exists a multi-party communication complexity problem, for which the protocol assisted by states which violate the inequality is more efficient than any classical protocol. Moreover, for that advantage Bell’s inequality violation is a necessary and sufficient criterion. Thus, violation of Bell’s inequalities has a significance beyond that of a non-optimal-witness of non-separability.

Quantum communication complexity protocol with two entangled qutrits.

We formulate a two-party communication complexity problem and present its quantum solution that exploits the entanglement between two qutrits. We prove that for a broad class of protocols the entangled state can enhance the efficiency of solving the problem in the quantum protocol over any classical one if and only if the state violates Bells inequality for two qutrits.

Entangling Photons Radiated by Independent Pulsed Sourcesa

By pumping two or more downconversion crystals with a pulsed laser, it is experimentally feasible to obtain with nonnegligible probability one photon pair from each crystal within a pulse. Then, by registering the idlers in such a way that this does not provide path information, we observe that the signal photons emitted together with the idlers are projected onto the desired entangled state. The necessary condition for erasure of idler path information is that the idler filter bandwidth results in an idler coherence time that significantly exceeds the pump pulse length. We show the importance of this technique for photon correlation schemes that would permit one to perform “event-ready’’ two-photon Bell tests, entanglement swapping, and quantum teleportation and to obtain GHZ states. Entanglement is at the source of a number of pure quantum phenomena, such as the correlations violating Bell’s inequalities,’ quantum teleportation,2 GHZ correlations,j and various other nonclassical interference phen~mena .~ Entanglement between two or more particles was generally viewed as a consequence of the fact that the particles involved did originate from the same source or at least were interacting at some earlier time. However, it has first been suggested in seminal papers by Yurke and Stoler-’ that the correlations of particle detection events required for a Bell test can even arise for photons, or any kind of particle for that matter, originating from independent sources. What, though, are the operational procedures required to achieve such correlations? If we can observe violations of Bell’s inequality for (destructive) registrations of particles coming from independent sources, can we also entangle them in a nondestructive manner? Is this possible for particles that do not interact at all and that share no common past? What would be the requirements for an experimental realization of such a scheme? These questions will be discussed here. In general, the answers could be summed up in the following way:6 it turns out

Space-quest: experiments with quantum entanglement in space

Quantumentanglement is, according to Erwin Schrodinger in 1935, the essence of quantumphysics. It inspires fundamental questions about the principles of nature. By testing the entanglement of particles,we are able to ask fundamental questions about realism and locality in nature. Local realismimposes certain constraints in statistical correlations ofmeasurements onmulti-particle systems. Quantummechanics, however, predicts that entangled systems havemuch stronger than classical correlations that are independent of the distance between the particles and are not explicablewith classical physics.

Security of Quantum Key Distribution with entangled Qutrits.

The study of quantum cryptography and quantum entanglement have traditionally been based on two-level quantum systems (qubits). In this paper, we consider a generalization of Ekerts entanglement-based quantum cryptographic protocol where qubits are replaced by three-level systems (qutrits). In order to investigate the security against the optimal individual attack, we derive the information gained by a potential eavesdropper applying a cloning-based attack. We exhibit the explicit form of this cloner, which is distinct from the previously known cloners, and conclude that the protocol is more robust than those based on entangled qubits as well as unentangled qutrits.

Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement.

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.