Deliverables
The key realisation which lead to the emergence of the new field of quantum information processing is that quantum mechanics allows the processing of information in fundamentally new ways. But just as in classical information processing, errors occur in quantum information processing, and these have to be corrected. A fundamental breakthrough was the realisation that quantum error correction is in fact possible.
However most work so far has not been concerned with technological feasibility, but rather with proving that quantum error correction is possible in principle. Partner 4 described a error correction method for filtering out errors and ntanglement purification which can be experimentally implemented. - Partner 4 has also investigated what are the fundamental limitations in aligning the frames of reference of two distant parties, and signalling a direction when the frames are already aligned. Along similar lines, the problem of communicating chirality has also been investigated. Partner 4 discussed in detail this issue and introduced the natural concept of quantum gloves, i.e. rotationally invariant quantum states that encode as much as possible the concept of chirality. - Nonlocality is the basic aspect of quantum mechanics underlying quantum information and communication. The limits of quantum non-locality were investigated by Partner 4 by considering non local correlation in their full generality, not only those correlations that may be produced by quantum mechanics. What kinds of non-locality are present in quantum states? By studying the extremal points of the space of all multi-party probability distributions, in which all parties can make one of a pair of measurements, each with two possible outcomes, a necessary condition for classical non-local models to reproduce the statistics of all quantum states was found.
The condition generalizes and extends the results of Sveltichny and of Collins, Gisin, Popescu, Roberts and Scarani who showed that separable classical non-local models cannot reproduce the statistics of all multi-particle quantum states. This condition shows that the non-locality present in some entangled multi-particle quantum states is much stronger than previously thought.
It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are non-local, in the sense that a Bell inequality is violated. They cannot, however, be used for super-luminal signalling. It is also known that it is possible to write down sets of super-quantum correlations that are more non-local than is allowed by quantum mechanics, yet are still non-signalling. Viewed as an information theoretic resource, super-quantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks.
An intriguing question is why quantum mechanics does not allow these more powerful correlations. In order to shed light on the range of quantum possibilities by placing them within a wider context, Partner 4 investigated the set of correlations that are constrained only by the no-signalling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset.- Partner 4 considered the situation in which an observer internal to an isolated system wants to measure the total energy of the isolated system (this includes his own energy, that of the measuring device and clocks used, etc...). It was shown that he can do this in an arbitrarily short time, as measured by his own clock. This measurement is not subjected to a time-energy uncertainty relation.
The properties of such measurements were discussed in detail with particular emphasis on the relation between the duration of the measurement as measured by internal clocks versus external clocks. It has recently been shown that all causal correlations between two parties which output each one bit, a and b, when receiving each one bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and non-local correlations of the form a+b=xy mod 2. Partner 4 demonstrated that a single instance of the latter elementary non-local correlation suffices to simulate exactly all possible projective measurements that can be performed on the singlet state of two qubits, with no communication needed at all.- Partner 4 investigated also the concentration of multi-party entanglement by focusing on simple family of three-partite pure states, superpositions of Greenberger-Horne-Zeilinger states and singlets.
Despite the simplicity of the states, it was shown that they cannot be reversibly concentrated by the standard entanglement concentration procedure, to which they seem ideally
suited.
In the first year of the project, a work concerning the surface-plasmon assisted transmission of entangled photons attracted widespread attention. In that experiment the effect on the polarization entanglement of photon pairs passing through arrays of subwavelength holes was investigated. The optical transmission of these hole arrays is anomalously large. It is believed to be associated with the excitation and coupling of surface plasmons at both sides of the whole arrays. It was experimentally found that the polarization entanglement of the transmitted photons is essentially identical to that of the incident photons.
However, in presence of tight focusing of the beams on a hole array the polarization entanglement rapidly decreases. This effect is related to the non-local nature of the electronic excitation (plasmon) at the metal surfaces. This non-local character imprints "Welcher Weg" information on the photons, resulting in less entanglement. A second aspect is connected to the orbital-angular momentum (OAM) degree of freedom of a photon, and its entanglement in the case of a photon pair. The OAM degree of freedom is attractive since it provides a high-dimensional alphabet for quantum-information processing. In order to maximally exploit the high-dimensionality of OAM Hilbert space, photons carrying half-integer OAM in units of ?, were investigated. A major advantage of these half-integer states is that they are not cylindrically symmetric, in contrast to the integer states, and can be oriented, similar, in a way, as the polarization states in polarization entanglement. Partner 2 proposed a novel setup to investigate the entanglement of OAM states living in a high-dimensional Hilbert space.
Non-integerspiral phase plates in spatial analysers were incorporated, enabling in this way the use of only two detectors. The two-photon states produced in the present setup are not confined to a 2x2 dimensional Hilbert space and this allows the probing of correlations in a high-dimensional space. In this setup Partner 2 could measure the quantum correlations while rotating the spiral phase plates contained in both the signal and idler arms. Parabolic coincidence fringes were observed in accord with theory. The coincidence fringes are shown to only depend on the relative orientation of the spiral phase plates in signal and idler arms.
These states were used to perform a Bell-type measurement on entanglement of spatial degrees of freedom, employing two analyser/detector combinations only. It is well known that, in the proper limit, integer orbital angular momentum is conserved in parametric down conversion. Moreover, this conservation rule also applies to the non-integer case. The theoretical value of the CHSH version of the Bell parameter equal to S=3.2, while this parameter cannot exceed the value 2v2 for qubits (Cirelsons bound). In parallel the measured value of the S-parameter beyond Cirelsons bound, namely S=3.07+/-0.06, corresponds to four standard deviations above the value 2v2.
The realization of a new scheme for generating polarization-entangled photon pairs represents one of the most interesting achievements of the ATESIT project. The high brilliance source realized in the Laboratory of Rome consists of a type-I crystal which operates in an interferometric scheme where all the photon couples emitted at a certain wavelength and belonging to the phase matching cone take part in the entanglement and can be measured. The source is given by a single arm interferometer operating with a Type-I NL crystal, which is excited in two opposite directions by a back-reflected UV pump beam. The generation of a 2-photon linear polarization entangled beam is given by the quantum superposition of the states created by Spontaneous Parametric Down Conversion (SPDC) in the opposite directions k and - k, the last one after back-reflection and suitable phase and polarization transformations. A 213- Bell's inequalities violation was obtained in this configuration and the characteristics of brightness and robustness of the source were confirmed by the fact that more than Ü 106 entangled photon pairs per second are generated by this source with 100mW pump power. This source represents the ideal solution to generate in principle any kind of entangled mixed state with tunable degrees of entanglement and mixedness. Moreover, tunable non maximally entangled states are easily produced by this source without postselection.
Nonlocality tests performed with this source may have a particular significance regarding the possible collection of the whole set of entangled photon pairs belonging to the phase matching cone. Besides Bell�s inequalities, it was possible to give the first experimental demonstration of the Hardy�s ladder proof for a large number of logical steps of the theorem. Testing a large number of steps implies a critical handling of increasingly large statistical samples with rapidly increasing exactness. Experimentally, this requires a high-stability, high-brilliance SPDC source able to generate entangled photon pairs with a high quantum efficiency. The peculiar properties featured by the high brilliance source allowed the substantial accomplishment of such endeavor.
Precisely by the recursive test of 20 ladder's steps a fraction as large as 41% of entangled photon pairs giving a contradiction with local realism was attained. By this source the properties of several relevant families of entangled mixed states can be generated and investigated, as said. Consistently with the above considerations, a patchwork technique, consisting of a sequence of different local operations, has been applied to the realization of the Werner states and the maximally entangled mixed states (MEMS), with variable mixing parameters. These states have been fully characterized by quantum tomography and their non local properties have been also tested. An interesting example of the fruitful joint collaboration of Partner 1 with Partner 3, based on the use of this source, was the first experiment of entanglement detection based on the measurement of an entanglement witness, which is achieved with a minimal number of local measurement settings. Polarized photons in Werner states have been used to perform this test, with perfect agreement with the theoretical predictions.
Finally, by taking advantage of its peculiar spatial characteristics and flexibility in terms of state generation, two photon states simultaneously entangled in polarization and linear momentum (hyper-entangled states), have been produced by the same system. Besides polarization entanglement, momentum entanglement is realized with high phase stability by selecting two symmetric pairs of correlated directions within the conical emission of the type I crystal adopted to generate the parametric fluorescence. The importance of these states in quantum information (QI) resides on the fact that they represent a way to overcome the intrinsic limit of SPDC where no more than one photon pair is created time by time within each microscopic annihilation-creation process. Some QI tasks can be realized by using these states. As an example, in the case of hyper-entangled states, the complete analysis of the four orthogonal Bell states with 100\% efficiency, a result otherwise impossible to achieve with standard linear optics, represents a fundamental tool for many QI objectives. Partner 1, in collaboration with Partner 3, investigated an experimental method to engineer arbitrary pure states of qu-dits, namely d-level quantum systems, i.e. qutrits (d = 3) and ququads (d = 4), using a single nonlinear crystal and linear optical devices as phase waveplates. Hyper-entangled states have been completely characterized in the laboratory of Rome and recently the nonlocal behaviour of these states has been verified by an 'all versus nothing' test of local realism, which represents a generalization of the GHZ to the case of two entangled particles and two observers.
- Two photon entanglement in doped Photonic Crystals. Giantly enhanced cross-phase modulation with suppressed spectral broadening is predicted between optically-induced dark-state polaritons whose propagation is strongly affected by photonic bandgaps of spatially periodic media with multilevel dopants. Partner 5 demonstrated that this mechanism is capable of fully entangling two single-photon pulses with high fidelity.
- Generation and Communication of Photon-Photon and Atom-Atom Entangled States. Partner 5 introduced two schemes for generation and transfer of photon-photon and atom-atom entanglement. A method was proposed to achieve a large conditional phase shift of a probe field in the presence of a single-photon control field. This scheme allows, in principle, high-fidelity state transfer from the entangled dissociated fragments to light, thereby producing a highly correlated photon pair.
- Towards High-Fidelity Two-Photon Quantum Communications. Two alternative schemes for highly efficient nonlinear interaction between weak optical fields were proposed by Partner 5. The first scheme is based on the attainment of electromagnetically induced transparency simultaneously for two fields via transitions between magnetically split F = 1 atomic sublevels, in the presence of two driving fields. The second scheme relies on simultaneous electromagnetically - and selfinduced transparencies of the two fields.
- Dynamical Control of Decay and Decoherence in Complex Quantum Systems.
-- The impediment towards the successful development of the field of quantum information (QI) is decoherence, i.e., the loss of entanglement by the effect of the environment on the systems of interest. An important challenge is that of QI engineering, by entanglement and decoherence control, in complex systems, such as unimolecular and bimolecular systems that can simultaneously handle large amounts of QI. Partner 5 gave a unified theory of dynamically modified decay and decoherence in driven quantum systems that are coupled to arbitrary finitetemperature reservoirs and undergo random phase fluctuations. Decay acceleration by frequent measurements (interruptions of the coupling), known as the anti-Zeno effect (AZE) was argued to be much more ubiquitous than its inhibition in one- or two-level systems coupled to reservoirs (continua). In multilevel systems, frequent measurements cause accelerated decay by destroying the multilevel interference, which tends to inhibit decay in the absence of measurements.
-- The realization of the position- and momentum-correlated atomic pairs that are confined to adjacent sites of two mutually shifted optical lattices and are entangled via laser-induced dipoledipole interactions was discussed by Partner 5. The Einstein-Podolsky-Rosen (EPR) paradox with translational variables is then modified by lattice-diffraction effects. This paradox can be verified to a high degree of accuracy in this scheme. A method for controlling the decoherence of a driven qubit which is strongly coupled to a reservoir, when the qubit resonance frequency is close to a continuum edge of the reservoir spectrum, was proposed. Partner 5 demonstrated that an appropriate sequence of nearly abrupt changes of the resonance frequency can protect the qubit state from decay and decoherence more effectively than the intuitively obvious alternative, which is to fix the resonance well within a forbidden bandgap of the reservoir spectrum, as far as possible from the continuum edge.
Because of the linearity of quantum mechanics an arbitrary quantum state cannot be 'cloned' perfectly, i.e. reproduced with 'fidelity' F=1 into M>1 states identical to the original. A second quantum impossibility process, based on the complete positivity character of any quantum operation, forbids the realization of a universal NOT gate i.e. one that flips exactly any input qubit into an orthogonal one. In the domain of quantum optics the cloning effect is directly associated to a photon amplification process in an Optical Parametric Amplifier (OPA). In the OPA N photons, prepared identically in an arbitrary quantum state |?> of polarization, are injected into the amplifier on the input mode k1.
The amplifier then generates on the same output 'cloning mode' M>N copies, or 'clones' of the input qubit |?>. Correspondingly, the OPA amplifier generates on the output'anticloning (AC) mode, k2 M-N states |?->, thus realizing a quantum NOT gate, which performs the operation to flip a qubit. It can exist simultaneously in the superposition |?>=a|0> + ß|1> of two logical states |0> and |1>, and it is impossible to find a universal transformation which would flip the original state |?> into the perpendicular state |?->=ß|0> - a|1> for all values of complex amplitudes a and ßi.e. for any (unknown) |?>.The first experimental realization of a universal quantum machine performing the best possible approximation of an anti-unitary operation, the Universal NOT (U-NOT) transformation was given in Rome.
The system adopted was a quantum self-injected optical parametric amplifier (QIOPA) of entangled photon states. An important consideration in the field of quantum information theory is which physical transformations to the state of a quantum system are allowed. The investigation of these universal optimal transformations, which are also called universal quantum machines, is important since it reveals bounds on optimal manipulations of information with quantum systems.
Theoretically it can be useful to design new algorithms and protocols, whereas experimental realizations witness an improvement in the manipulation of small ensembles of qubits. Partner 1 has been interested in realizing the quantum analogues of two fundamental processes of classical information: the NOT gate and the cloning (copying) machine. The quantum forms of these two transformations cannot be realized perfectly. However their optimal realizations, with the minimum possible noise, present interesting features.
The quantum U-NOT gate is deeply related to the quantum estimation of an unknown state while the optimal quantum cloning is the best way to redistribute the initial information content into many parts. Quantum cryptography bases its security on the impossibility to clone unknown quantum states. Nevertheless, since experimental imperfections have to be taken into account, there exist some bounds on the noise value that assure a secure communication.
These bounds depend on the information that a spy can obtain interacting with the quantum system. The optimal quantum cloning is the best eavesdropping attack on some quantum cryptography protocols It is the best trade-off between disturbance and acquired knowledge. These two quantum machines, the U-NOT gate and the optimal quantum cloning, were contextually realized by adopting the process of stimulated emission generated by a single photon into an optical parametric amplifier(OPA).
The objective of realizing a photon-number-resolving detector didnt give a conclusive result within the development of the ATESIT project. The relevance of this objective resides on the fact that linear optics computation requires photon number resolving detectors to achieve the scalability of computation. The excitation of a photocatode with an evanescent wawe represented originally a new kind of coupling between radiation and photocatode to enhance the quantum efficiency qe. In the original idea the evanescent wawe is coupled to the photocathode with a displacement of the reflected beam in the direction of the interface. Since is much larger than the photocatode thickness, a relevant enhancement of the photon absorption cross section is expected.
This effect was experimentally verified by Partner 1 with different photocathodes and a value of qe 20% was measured with an enhancement = 2. The capability of this device to discriminate different photon numbers was tested by a standard Ou-Mandel interferometer operating with twin photons generated at 532 nm. A high value of visibility = 100% was measured but some signals due to the overlapping effect of the one and two photon distributions were discarded. As a result the effective value of qe was lowered. In order to improve the detector photon discrimination several possible solutions have been tested. A new detector was adopted to achieve a better discrimination between Fock states. It was given by a hybrid photodiode that ensures a higher intrinsic photon number resolution due to the peculiar single step internal amplification.
The intrinsic amplification of the hybrid photodiode (HPD)corresponded to 3500 electrons / photoelectrons. Lighting the chatode with a strongly attenuated pulsed laser, the photon-number discrimination of the tube was tested by identifying the nphotoelectron output signal and analysing the respective amplitude spectra. In spite of the fact that HPD response curves present narrow peaks of the n-photoelelectron, photon number resolution was spoiled for an increasing number of incident photons by a growing-up of a broad background between different peaks. This phenomenon was attributed to the backscattering of the accelerated photoelectrons when inpinging on the diode and provides a partial deposition of their energy in the active diode region. Since the attenuation of the backscattering effect is highly critical to achieve a better photon-number resolution, strategies to reduce its influence should be studied and pursued.
A qubit teleportation, experimentally demonstrated by Partner 1, in collaboration with Partner 4 with an unprecedented large 'fidelity' (F0.95) was one of the first ATESIT results. It is based on the concept of 'entanglement of one photon with the vacuum' by which each qubit can be physically implemented by a two dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the QED 'vacuum' and the 1-photon state. The relevant conceptual novelty introduced here consists of the fact that the field's modes rather than the photons associated with them are taken as the information carriers, qubits. It is worth noting that, differently from the standard scheme of quantum bit teleportation, the present realization has the advantage of avoiding the difficult implementation of the final stage of QST: the unitary transformations U restoring the exact input qubit at Bob's site under Alice's control through the QST classical channel.
The active qubit teleportation process was realized in Rome by adopting this vacuum-1 photon configuration. In that case the main problem was to switch under single-photon excitation the high-voltage pulses driving the electro-optic Pockels-cells (EOP) which implemented the necessary U-unitaries at Bob's site. Of course, in order to preserve an appreciable QST fidelity it must be: T<
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