Álvaro J. Almeida

Interference in a Quantum Channel Due to Classical Four-Wave Mixing in Optical Fibers

The second-order coherence function for idler photons generated through stimulated four-wave mixing (FWM) is theoretically derived, considering both spontaneous and stimulated Raman contributions. Two distinct cases and two different power regimes are analyzed. First, we consider that the idler wave is fully generated inside the fiber. In a second scenario, we admit that at the fiber input there exist a quantum channel and idler photons will be created at that frequency through the combined processes of FWM and Raman scattering. Results show that for the first case, in a low power regime, the idler photons follow a thermal statistics. In a moderate power regime, the statistics of the generated idler wave presents a Poissonian distribution. Results also show that in the second case, in a low power regime, the statistics of the input quantum channel goes from a Poissonian statistics at the fiber input to a thermal statistics at the fiber output. Findings show that in a moderate power regime, the quantum channel maintains its Poissonian distribution through fiber propagation.

Noise and measurement errors in a practical two-state quantum bit commitment protocol

We present a two-state practical quantum bit commitment protocol, the security of which is based on the current technological limitations, namely the nonexistence of either stable long-term quantum memories or nondemolition measurements. For an optical realization of the protocol, we model the errors, which occur due to the noise and equipment (source, fibers, and detectors) imperfections, accumulated during emission, transmission, and measurement of photons. The optical part is modeled as a combination of a depolarizing channel (white noise), unitary evolution (e.g., systematic rotation of the polarization axis of photons), and two other basis-dependent channels, namely the phase- and bit-flip channels. We analyze quantitatively the effects of noise using two common information-theoretic measures of probability distribution distinguishability: the fidelity and the relative entropy. In particular, we discuss the optimal cheating strategy and show that it is always advantageous for a cheating agent to add some amount of white noise - the particular effect not being present in standard quantum security protocols. We also analyze the protocols security when the use of (im)perfect nondemolition measurements and noisy or bounded quantum memories is allowed. Finally, we discuss errors occurring due to a finite detector efficiency, dark counts, and imperfect single-photon sources, and we show that the effects are the same as those of standard quantum cryptography.

Implementation of a two-state quantum bit commitment protocol in optical fibers

We demonstrate experimentally the feasibility of a two-state quantum bit commitment protocol, which is both concealing and partially binding, assuming technological limitations. The security of this protocol is based on the lack of long-term stable quantum memories. We use a polarization-encoding scheme and optical fiber as a quantum channel. The measurement probability for the commitment is obtained and the optimal cheating strategy demonstrated. The average success rates for an honest player in the case where the measurements are performed using equal bases are 93.4%, when the rectilinear basis is measured, and 96.7%, when the diagonal basis is measured. The rates for the case when the measurements are performed in different bases are 52.9%, when the rectilinear basis is measured, and 55.4% when the diagonal basis is measured. The average success rates for the optimal cheating strategy are 80% and 73.8%, which are way below the success rates of an honest player. Using a strict numerical validity criterion, we show that, for these experimental values, the protocol is secure.

Using quantum technologies to improve fiber optic communication systems

We discuss the near future impact that recent developments of quantum technologies can have in the field of fiber optic communication systems. The ability to generate, manipulate, transmit, and detect a single or very few photon(s) may open new routes that can trigger a completely new generation of communication systems. We show that quantum technologies can address two of the more challenging problems communication engineers face nowadays: capacity and security. Indeed, by radically decreasing the number of photons used to encode each bit of information, we can more efficiently explore the full capacity to carry information of optical fibers. Moreover, by encoding information in individual or very few photons, we can take advantage of the quantum laws to add new functionalities to communication systems. Secrecy is the more obvious one, but a completely new set of functionalities can be added at the physical layer considering the peculiarities of quantum laws that rule transmission and detection.

Polarization-entangled photon pairs using spontaneous four-wave mixing in a fiber loop

We generate polarization-entangled photon pairs in the 1550-nm wavelength telecom band, using spontaneous four-wave mixing in a highly nonlinear fiber loop. With accidental coincidences subtracted, we obtain coincidence fringes with visibilities greater than 86%, and thus observe a violation of Clauser, Horne, Shimony and Holt (CHSH) inequality by 2.7 standard deviations. The experimental setup is built using only fiber connections, which contribute to its long time stability.

Single-photon source using stimulated FWM in optical fibers for quantum communication

A single-photon source based on the stimulated four-wave mixing (SFWM) process in optical fibers is presented. At the output of the source, the state of polarization (SOP) of the photons can be adjusted in order to obtain any linear polarization. A theoretical model to describe the average photon counts recorded in the avalanche photodiodes (APDs) is presented. The experimental results show an accurate detection of two non-orthogonal linear SOPs after propagation through a 60 km quantum channel, and good agreement with theory. This source, operating in a low power regime, can be used for quantum key distribution (QKD) using polarization-encoding in quantum communications.

Calculation of the number of bits required for the estimation of the bit error ratio

We present a calculation of the required number of bits to be received in a system of communications in order to achieve a given level of confidence. The calculation assumes a binomial distribution function for the errors. The function is numerically evaluated and the results are compared with the ones obtained from Poissonian and Gaussian approximations. The performance in terms of the signal-to-noise ratio is also studied. We conclude that for higher number of errors in detection the use of approximations allows faster and more efficient calculations, without loss of accuracy.

A brief review on quantum bit commitment

In classical cryptography, the bit commitment scheme is one of the most important primitives. We review the state of the art of bit commitment protocols, emphasizing its main achievements and applications. Next, we present a practical quantum bit commitment scheme, whose security relies on current technological limitations, such as the lack of long-term stable quantum memories. We demonstrate the feasibility of our practical quantum bit commitment protocol and that it can be securely implemented with nowadays technology.

Theoretical Analysis of Multimodal Four-Wave Mixing in Optical Microwires

Optical fiber microwires (OFMs) are nonlinear optical waveguides that support several spatial modes. The multimodal generalized nonlinear Schrödinger equation (MM-GNLSE) is deduced taking into account the linear and nonlinear modal coupling. A detailed theoretical description of four-wave mixing (FWM) considering the modal coupling is developed. Both, the intramode and the intermode phase-matching conditions is calculated for an optical microwire in a strong guiding regime. Finally, the FWM dynamics is studied and the amplitude evolution of the pump beams, the signal and the idler are analyzed.

Optical quantum communications: an experimental approach

Quantum laws can be used to implement secure communication channels; this has been named quantum cryptography. In quantum cryptography the security does not depend of limited computational power, but is inherent to the laws that govern the propagation and detection of single and entangled photons. We show how single and entangled photon-pairs can be efficiently generated using four-wave mixing in optical fibers. We analyze the source statistics, degree of entanglement and impact of spontaneous Raman scattering. By coding information in the photons polarization we are able to transmit quantum information over 20 km of standard single mode fiber.