Twisted Photons: New Quantum Perspectives in High Dimensions

Quantum information science and quantum information technology have seen a virtual explosion world-wide. It is all based on the observation that fundamental quantum phenomena on the individual particle or system-level lead to completely novel ways of encoding, processing and transmitting information. Quantum mechanics, a child of the first third of the 20th century, has found numerous realizations and technical applications, much more than was thought at the beginning. Decades later, it became possible to do experiments with individual quantum particles and quantum systems. This was due to technological progress, and for light in particular, the development of the laser. Hitherto, nearly all experiments and also nearly all realizations in the fields have been performed with qubits, which are two-level quantum systems. We suggest that this limitation is again mainly a technological one, because it is very difficult to create, manipulate and measure more complex quantum systems. Here, we provide a specific overview of some recent developments with higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum (OAM) states of photons and possible applications in quantum information protocols. Such states form discrete higher-dimensional quantum systems, also called qudits. Specifically, we will first address the question what kind of new fundamental properties exist and the quantum information applications which are opened up by such novel systems. Then we give an overview of recent developments in the field by discussing several notable experiments over the past 2-3 years. Finally, we conclude with several important open questions which will be interesting for investigations in the future.Comment: 15 pages, 7 figure

Generic Bell inequalities for multipartite arbitrary dimensional systems

We present generic Bell inequalities for multipartite multi-dimensional systems. The inequalities that any local realistic theories must obey are violated by quantum mechanics for even-dimensional multipartite systems. A large set of variants are shown to naturally emerge from the generic Bell inequalities. We discuss particular variants of Bell inequalities, that are violated for all the systems including odd-dimensional systems.Comment: Accepted in Phys. Rev. Let

Orbital angular momentum of photons and the entanglement of Laguerre-Gaussian modes

The identification of orbital angular momentum (OAM) as a fundamental property of a beam of light nearly twenty-five years ago has led to an extensive body of research around this topic. The possibility that single photons can carry OAM has made this degree of freedom an ideal candidate for the investigation of complex quantum phenomena and their applications. Research in this direction has ranged from experiments on complex forms of quantum entanglement to the interaction between light and quantum states of matter. Furthermore, the use of OAM in quantum information has generated a lot of excitement, as it allows for encoding large amounts of information on a single photon. Here we explain the intuition that led to the first quantum experiment with OAM fifteen years ago. We continue by reviewing some key experiments investigating fundamental questions on photonic OAM and the first steps into applying these properties in novel quantum protocols. In the end, we identify several interesting open questions that could form the subject of future investigations with OAM.Comment: 17 pages, 7 figures; close to accepted versio

Trusted Noise in Continuous-Variable Quantum Key Distribution: a Threat and a Defense

We address the role of the phase-insensitive trusted preparation and detection noise in the security of a continuous-variable quantum key distribution, considering the Gaussian protocols on the basis of coherent and squeezed states and studying them in the conditions of Gaussian lossy and noisy channels. The influence of such a noise on the security of Gaussian quantum cryptography can be crucial, even despite the fact that a noise is trusted, due to a strongly nonlinear behavior of the quantum entropies involved in the security analysis. We recapitulate the known effect of the preparation noise in both direct and reverse-reconciliation protocols, as well as the detection noise in the reverse-reconciliation scenario. As a new result, we show the negative role of the trusted detection noise in the direct-reconciliation scheme. We also describe the role of the trusted preparation or detection noise added at the reference side of the protocols in improving the robustness of the protocols to the channel noise, confirming the positive effect for the coherent-state reverse-reconciliation protocol. Finally, we address the combined effect of trusted noise added both in the source and the detector.Comment: 25 pages, 9 figure

Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

Device-independent dimension test in a multiparty Bell experiment

A device-independent dimension test for a Bell experiment aims to estimate the underlying Hilbert space dimension that is required to produce given measurement statistical data without any other assumptions concerning the quantum apparatus. Previous work mostly deals with the two-party version of this problem. In this paper, we propose a very general and robust approach to test the dimension of any subsystem in a multiparty Bell experiment. Our dimension test stems from the study of a new multiparty scenario which we call prepare-and-distribute. This is like the prepare-and-measure scenario, but the quantum state is sent to multiple, non-communicating parties. Through specific examples, we show that our test results can be tight. Furthermore, we compare the performance of our test to results based on known bipartite tests, and witness remarkable advantage, which indicates that our test is of a true multiparty nature. We conclude by pointing out that with some partial information about the quantum states involved in the experiment, it is possible to learn other interesting properties beyond dimension.Comment: 10 pages, 2 figure

A qutrit Quantum Key Distribution protocol with better noise resistance

The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.Comment: 11 page

Quantum spiral bandwidth of entangled two-photon states

We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state in spontaneous parametric downconversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down converting crystal and waist of the pump beam. The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.Comment: 10 pages, 3 figure