Quantum Computation and Information Seminar 

The ability to generate, manipulate, transmit and detect single-photons can open new routes that can trigger a complete new generation of optical communication systems. We show that quantum technologies can indeed address two of the more challenging problems that communication engineers face nowadays: capacity and security. We discuss critical issues in the implementation of quantum communication systems over installed optical fibers. We use stimulated four-wave mixing to generate single photons inside optical fibers, and by tuning the separation between the pump and the signal we adjust the average number of photons per pulse. We report measurements of the source statistics and show that it goes from a thermal to Poisson distribution with the increase of the pump power. We generate entangled photons pairs through spontaneous four-wave mixing. We present optimum configurations to increase the degree of entanglement. We discuss the impact of polarization rotation, attenuation and Raman scattering. We encode information in the photons polarization and discuss control methods to compensate for polarization random rotation during propagation. We discuss the implementation of single-photons systems in installed standard single-mode fibers.

One manifestation of the exotic nature of quantum theory is the existence of correlations between systems that would be impossible within any classical theory. Quantum correlations, for instance in the form of quantum entanglement or quantum nonlocality, are considered a key ingredient for the overachieving performance of quantum systems at information processing tasks. Despite their importance, the set of quantum correlations is only known in very simple situations. We can impose a bound on the strength of quantum correlations by assuming that they obey the "no-signalling principle", i.e., they are compatible with restrict relativity by not allowing information to be sent instantaneously. But this principle alone is not enough: some no-signalling correlations are not possible in a quantum world.

In this talk I will present a very simple (almost naive!) multi-party game, "Guess your neighbour's input", where the best performance of the players is a signature of the kind of physical resources they use (classical, quantum or no-signalling). I show that we can distinguish classical/quantum theories from no-signalling ones, but only in the case we have more than two players. This indicates the existence of a generalized no-signalling principle for the multipartite setting.

I will discuss the relevance of quantum simulations for reproducing different aspects of quantum physics: nonrelativistic and relativistic quantum dynamics, physical and unphysical quantum operations, as well as strong and ultrastrong light-matter couplings. I will give examples in the context of trapped-ion and circuit QED technologies.

In this talk I am going to present an approach based on the Wyner information-theoretical model. This model assumes that there is no preshared secret key. The main idea is that quantum resources can improve simultaneously the secrecy of the key generated by a pseudo-random number generator and the secrecy of the tag obtained with a hidden hash function (integrity control). As a result, quantum key distribution (QKD) becomes a fully quantum protocol. Most of my presentation is based on the article ‘‘Improving classical authentication over a quantum channel’’ (joint with F .M. Assis, P. Mateus and Y. Omar). This work solves the problem of quantum authentication of classical messages. The methodology that has been used is based on the no-cloning theorem and single-qubit transfer. One of the most important results of the paper is proposing an optimal authentication scheme for QKD that includes almost-fair random number generation (the result is hardware-independent).

In this talk we give a quantum statistical interpretation for the bracket polynomial state sum K and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones polynomial. This algorithm is useful for its conceptual simplicity, and it applies to all values of the polynomial variable that lie on the unit circle in the complex plane. Letting $C(K)$ denote the Hilbert space for this model, there is a natural unitary transformation $U$ from $C(K)$ to itself such that $K=tr(U)$. The quantum algorithm arises directly from this formula via the Hadamard Test. We then show that the framework for our quantum model for the bracket polynomial is a natural setting for Khovanov homology. The Hilbert space $C(K)$ of our model has basis in one-to-one correspondence with the enhanced states of the bracket state summmation and is isomorphic with the chain complex for Khovanov homology with coefficients in the complex numbers. We show that for the Khovanov boundary operator d defined on $C(K)$ we have the relationship $dU+Ud=0$. Consequently, the unitary operator $U$ acts on the Khovanov homology, and we therefore obtain a direct relationship between Khovanov homology and this quantum algorithm for the Jones polynomial. The formula for the Jones polynomial as a graded Euler characteristic is now expressed in terms of the eigenvalues of $U$ and the Euler characteristics of the eigenspaces of $U$ in the homology. The quantum algorithm given here is inefficient, and so it remains an open problem to determine better quantum algorithms that involve both the Jones polynomial and the Khovanov homology.

In my talk we will show that within a non-relativistic quantum-mechanical model of a Universe (the q-Universe) the statistical temperature emerges as a consequence of quantum entanglement. In particular, I will model the q-Universe as a system of interacting spin-1/2 particles described by a specific Hamiltonian (e.g. the Ising Hamiltonian). The q-Universe is assumed to be in a pure state of its Hamiltonian. Iwill show that any (almost) sub-system of the q-Universe is in a mixed state described by a density operator such that probabilities of outcomes of measurements in the energy eigenbasis of the sub-system can be very well approximated by the Boltzmann distribution.

This seminar will be about quantum simulation with dressed optical lattices. I will first define and motivate the concept of quantum simulation and present some of the first theoretical proposals and experimental realizations of quantum simulators. I will move on to give an introduction to the physics of optical lattices and state-dependent optical lattices. Then, I will present some of the quantum simulator proposals we have put forth using this technology.

Continuation of the previous seminar.

In the current Quantum Key Distribution (QKD) proposals it is possible to generate a secret key and distribute it with the involved parties separated in physical terms. This possibility opens the possibility of structuring a solution to the classical cryptography problem of key distribution with reduced interaction among involved parties. Among other proposals to address this issue is the Eckert 91 protocol which will be in the scope of this report. Proposed in 1991 by A. Eckert it is an entanglement based protocol. The security assurance of entanglement based protocols is based on the impossibility of an eavesdropper to clone a message without destroying it. As such the receiver has the possibility to detect eavesdropping and this is a major advantage of this type of protocols. In the end a security proof will be described.

One of key differences of quantum mechanics and classical physics is the inability to perform all pairs of measurements simultaneously in quantum domain. The most prominent examples are position-momentum observables or spin components. In the talk I aim to show the analysis of simultaneous measurements (observables) in simplest qubit case. The talk will also touch generalization of the notion of joint measurability (and coexistence) of observables to more general quantum measurement devices.

In this talk I will discuss different scenarios in natural and artificial systems in which decoherence -- as an intrinsic part of the dynamics -- can be exploited for enhancing quantum processes in the context of charge and energy transfer, as well as for information processing, in disordered and noisy media.

We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-1/2 centers, such as quantum dots or superconducting qubits, can implement a CZ gate (universal for quantum computation) between them. This occurs deterministically in a single scattering event, hence with no need for any post-selection or iteration, and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.

This talk provides an overview of one of the central problems in communication engineering in the last 10 years, whose solution allows us now to reach the 1 Gbps frontier in wireless systems such as LTE Advanced and WiMax. The capacity limits set by Shannon in 1948 for digital transmission were reached in 1993 and 1995 after the discovery of turbo-codes and low-density parity-check codes. While this put an end to an era in coding theory, a new door was opened in the late 90s for wireless channels: multiple-input multiple output (MIMO). It was soon mathematically proved that increasing the number of antennas both at the transmitter and at the receiver would increase the capacity of the radio link. However, this gain comes at the expense of a much higher algorithmic complexity at the receiver side. The mathematical underlying detection problem is the closest vector problem (CVP) in a lattice. The problem had been mostly investigated in algorithmic number theory and much of the progress made in signal processing in communications came in fact from the re-discovery of algorithms known in the communities of algorithmic number theory and cryptography. The talk will describe several approximate and exact solutions to CVP, emphasising the geometric manipulation of lattices that is carried out by the most relevant algorithms: maximum likelihood detection, zero-forcing, minimum mean square error, successive detection, sphere decoding and lattice reduction. A novel approach to the problem will also be presented, which maps the problem onto a graph-based path minimisation problem.

We shall attempt to give a non-rigorous and informal review about the implications of combining general relativity and quantum mechanics. The main focus will be on two topics, the Problem of Time and the Black-Hole Information Paradox, and their implications on the structure of both QM and GR. Some other relevant issues will also be mentioned, like quantum cosmology and the Measurement Problem. The goal of the lecture is to emphasize the main "points of friction" between GR and QM, and to illuminate why the gravity quantization program is nontrivial.

Despite its often praised unconditional security, quantum key distribution (QKD) also relies on assumptions. Some of them are quite natural, such as the validity of quantum mechanics, the existence of true random number generators, or the assumption that the legitimate users are well shielded from the eavesdropper. Other assumptions, such as considering that the honest parties have an accurate and complete description of their physical devices, are more severe. Obviously, if the functioning of the real setup differs from that considered in the mathematical model, this may become completely vulnerable to new types of attacks not covered by the security proof. Indeed, quantum hacking against commercial QKD systems, particularly detector side channel attacks, have emerged as a hot topic. Here, we investigate a simple solution to this problem — measurement device independent QKD. It not only removes all detector side channels, but also doubles the secure distance with conventional lasers. In comparison to full device independent QKD (diQKD), our scheme does not require detectors of near unity detection efficiency in combination with a qubit amplifier or a quantum non-demolition measurement of the number of photons in a pulse, but can be implemented with standard optical components with low detection efficiency and highly lossy channels. Furthermore, its key generation rate is many orders of magnitude higher than that based on full diQKD.

In this talk I will discuss how the theoretical framework developed in quantum information science may be used to quantify coherence and performance of photosynthetic systems.

The Polya number characterizes the recurrence of a random walk. We apply the generalization of this concept to quantum walks which is based on a specific measurement scheme. The Polya number of a quantum walk depends, in general, on the choice of the coin and the initial coin state, in contrast to classical random walks where the lattice dimension uniquely determines it. We analyze several examples to depict the variety of possible recurrence properties. For 2D square lattices the Grover walk exhibits localization and thus is recurrent, except for a particular initial state for which the walk is transient. We generalize the Grover walk to show that one can construct in arbitrary dimensions a quantum walk which is recurrent. This is in great contrast with classical walks which are recurrent only for the dimensions $d=1,2$. The 2D Fourier walk is recurrent except for a two-dimensional subspace of the initial states. In order to better understand the role of dimensionality in the recurrence properties, one can consider a triangular lattice. The three-state Grover walk on a two-dimensional triangular lattice does not lead to trapping (localization) or recurrence to the origin, in sharp contrast to the corresponding walk on the two-dimensional square lattice. In general, on a triangular lattice only a special subclass of coin operators can lead to recurrence, and there are no coins that would lead to localization. The definition for the Polya number can be extended to continuous-time quantum walks, as well. For the timing of the measurements, a Poisson process as well as regular timing are discussed. We examine various graphs, including the ring, the line, the higher-dimensional integer lattices, and a number of other graphs, and we calculate their Polya number. We find that the speed of decay for the probability at the origin is the key for recurrence.

Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Recently, this idea of "semi-quantum" has been incorporated to quantum secret sharing [Phys.Rev. A 82, 022303 (2010)], where a quantum participant, Alice, can share a secret key with two classical participants so that they can collaborate to recover the secret, but none of them can do alone. However, in the protocol, a three-particle maximally‚ entangled state plays a crucial role. Nevertheless, multipartite entangled states are generally difficult to prepare in experiment. Therefore, in this talk, we present a new protocol of semi-quantum secret sharing‚ where a quantum participant can share a secret key with two classical participants without using any entanglement. The presented protocol is also showed to be secure against eavesdropping.

We present recent experimental work related with the generation of single and entangled photon pairs. We analyze the source statistics and the degree of entanglement. We discuss techniques to code information in the photons polarization and to compensate for polarization fluctuations due to propagation. We present a method to estimate the QBER in communication systems based on polarization encoding.

I consider quantum systems based on a canonical extension of Heisenberg's algebra. Such systems can be regarded as the non-relativistic limit of a one-particle sector of some noncommutative quantum field theory, or alternatively, as the quantization of systems coupled to external fields. I advocate that the Weyl-Wigner formulation is better suited to deal with such system in comparison with the usual Schrodinger formulation. The corresponding Weyl calculus for observables is developped and the representatives of states are defined. These are called noncommutative Wigner functions. As an application, I consider a Brownian particle interacting with a noncommutative gas at thermal equilibrium. I estimate the time for the transition from noncommutative to ordinary quantum mechanics and compare it with the typical time scale of the quantum-classical transition.