We revisit the physics of hole-conjugate Fractional Quantum Hall (FQH) phases characterized by counter-propagating edge channels at filling factors above 1/2. We propose a minimal and intuitive model that successfully accounts for all experimentally observed features, introducing a paradigm shift in the understanding of hole-conjugate edge channel dynamics. Our model identifies inter-channel charge equilibration as the sole essential mechanism, eliminating the need to invoke charge modes or upstream neutral modes, as posited in prior theoretical frameworks. By incorporating fictitious reservoirs along the edge, the model qualitatively and quantitatively reproduces key observations, including counterintuitive upstream effects previously misattributed to neutral modes. We provide predictions for electrical and thermal conductance as well as current noise for filling factors 2/3 and 3/5. Additionally, we address the case of non-dissipative reservoirs, which preserve conductance properties while exhibiting infinite thermal relaxation lengths

Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional qubits.

Single-electron sources are an essential component of modern quantum nanoelectronic devices. Owing to their high accuracy and stability, they have been successfully employed for metrology applications, studying fundamental matter interactions and more recently for electron quantum optics. They are traditionally driven by state-of-the-art arbitrary waveform generators that are capable of producing single-electron pulses in the sub-100 ps timescale. In this work, we use an alternative approach for generating ultrashort electron wavepackets. By combining several harmonics provided by a frequency comb, we synthesise Lorentzian voltage pulses and then use them to generate electron wavepackets. Through this technique, we report on the generation and detection of an electron wavepacket with temporal duration of 27 ps generated on top of the Fermi sea of a 2-dimensional electron gas - the shortest reported to date. Electron pulses this short enable studies on elusive, ultrafast fundamental quantum dynamics in nanoelectronic systems and pave the way to implement flying electron qubits by means of Levitons.

We consider a two-particle interferometer, where voltage sources applied to ohmic contacts inject electronic excitations into a pair of copropagating edge channels. We analyze the impact of channel mixing due to inter-edge tunneling on the current noise measured at the output of the interferometer. Due to this mixing, the noise suppression typically expected for synchronized injecting sources is incomplete, thereby reducing the visibility of the interference. We investigate to which extent the impact of mixing on the noise visibility depends on different shapes of the voltage drives. Furthermore, we compare a simple model involving a single mixing point between the sources and the quantum point contact to the more realistic case of a continuous distribution of weak mixing points.

We study photoassisted transport for the edge states of a two-dimensional electron gas in the fractional quantum Hall regime, pinched by a single quantum point contact. We provide a general expression of the photoassisted current using a Keldysh-Floquet approach, when the AC drive is applied either directly to the edge states, or when it modulates the tunneling amplitude at the quantum point contact. Strikingly, for a simple cosine modulation of the tunneling amplitude, the phase shift of the second harmonic of the photoassisted current is directly related to the scaling dimension of the quasiparticle operators describing the fractional excitations. As the scaling dimension is intimately related to the statistics, our proposal of a gate modulation of the backscattered current provides a diagnosis of the statistics of Laughlin quasiparticles using a simple quantum point contact geometry.

Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot interferometers, but almost no quantum interference when transmitted via the propagating states of Mach-Zehnder interferometers. Here, using a novel interferometric approach, we demonstrate that anyons do keep quantum coherence while propagating. Performing two-particle time-domain interference measurements sensitive to the two-particle Hanbury Brown Twiss phase, we find 53 and 60% visibilities for anyons with charges e/5 and e/3. Our results give a positive message for the challenge of performing controlled quantum coherent braiding of anyons.

The progress of charge manipulation in semiconductor-based nanoscale devices opened up a novel route to realise a flying qubit with a single electron. In the present review, we introduce the concept of these electron flying qubits, discuss their most promising realisations and show how numerical simulations are applicable to accelerate experimental development cycles. Addressing the technological challenges of flying qubits that are currently faced by academia and quantum enterprises, we underline the relevance of interdisciplinary cooperation to move emerging quantum industry forward. The review consists of two main sections: Pathways towards the electron flying qubit: We address three routes of single-electron transport in GaAs-based devices focusing on surface acoustic waves, hot-electron emission from quantum dot pumps and Levitons. For each approach, we discuss latest experimental results and point out how numerical simulations facilitate engineering the electron flying qubit. Numerical modelling of quantum devices: We review the full stack of numerical simulations needed for fabrication of the flying qubits. Choosing appropriate models, examples of basic quantum mechanical simulations are explained in detail. We discuss applications of open-source (KWANT) and the commercial (nextnano) platforms for modelling the flying qubits. The discussion points out the large relevance of software tools to design quantum devices tailored for efficient operation.

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.

We consider an electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime, where the colliding electronic states are generated by applying voltage pulses (creating for instance Levitons) to ohmic contacts. The aim of this work is to investigate possible mechanisms leading to a reduced visibility of the Pauli dip, i.e., the noise suppression expected for synchronized sources. It is known that electron-electron interactions cannot account for this effect and always lead to a full suppression of the Hong-Ou-Mandel noise. Focusing on the case of filling factor ν = 2, we show instead that a reduced visibility of the Pauli dip can result from mixing of the copropagating edge channels, arising from tunneling events between them.

Graphene is a very promising test bed for the field of electron quantum optics. However, a fully tunable and coherent electronic beam splitter is still missing. We report the demonstration of electronic beam splitters in graphene that couple quantum Hall edge channels having opposite valley polarizations. The electronic transmission of our beam splitters can be tuned from zero to near unity. By independently setting the beam splitters at the two corners of a graphene p-n junction to intermediate transmissions, we realize a fully tunable electronic Mach-Zehnder interferometer. This tunability allows us to unambiguously identify the quantum interferences due to the Mach-Zehnder interferometer, and to study their dependence with the beam-splitter transmission and the interferometer bias voltage. The comparison with conventional semiconductor interferometers points toward universal processes driving the quantum decoherence in those two different 2D systems, with graphene being much more robust to their effect.

This paper investigated the pulse amplitude modulation (PAM) decomposition of a class of continuous phase modulation (CPM) signal, which has the property to be a single-side band.We used the PAM decomposition as a convenient solution to provide a large reduced complexity trellis detection to approach the theoretical optimal performance.Moreover, we developed an algorithm to obtain the necessary PAM pulses to approach the optimal performance bound using suboptimal receivers.The algorithm is generic; it can provide the results for any parameter combinations.The proposed demodulation system exhibits excellent performance with minimal complexity with respect to the maximum likelihood sequence detection (MLSD) optimal receiver.

We review noise measurements in quantum coherent semiconductor nanodevices. Quantum coherent conductors are characterised by their small size such that a carrier crossing the conductor preserves its phase coherence. This requires no inelastic energy exchange with photon, phonon, plasmons or other dynamical excitations and no phase averaging by random noise. Such highly quantum regime is best obtained at very low temperature. The quantum coherent regime can be realised in metals or in doped semiconductors of sub-micron size. Here, we concentrate on semiconductor nanodevices. Doped semiconductors and in particular 2D electron systems realised at the interface of modulation doped heterojunctions have enabled the realisation of Quantum Point Contacts, a key tool to test the physics of quantum noise. Shot noise played an important role in the development of new ideas in Condensed Matter. The analogy between the quantum noise of electrons transferred through a conductor and the noise of photons propagating in an optical medium has pushed towards the development of Electron Quantum Optics where quantum point contact was used to mimic optical beam splitters. We will see that quantum shot noise can also be used to measure the (fractional) charge of electronic carriers, to perform the energy spectroscopy of electronic excitations, to determine unambiguously the transmission probability of electronic quantum modes, to count the number of electron and hole generated by AC excitations and even to detect THz radiation.

This study revokes the performance of continuous phase modulation (CPM) able to generate a single-sideband (SSB) spectrum directly. This signal is analyzed in terms of modulation indices, pulse lengths, and pulse widths, all of which affect error probability, bandwidth, SSB property, and receiver complexity. The error probability performance is based on an approximation of the minimum Euclidean distance. A numerical power spectral density calculation for this particular SSB modulation in terms of the modulation index is presented. Reasonable tradeoffs in designing modulation schemes have been proposed using multi-objective optimization to ensure sizable improvements in bit error rate (BER), spectral efficiencies, and complexity without losing the property of being a SSB signal. Performance comparisons are made with known CPM schemes, e.g., Gaussian Minimum Shift Keying (GMSK) and Raised Cosine based CPM (RC).

Magnons enable the transfer of a magnetic moment or spin over macroscopic distances. In quantum Hall ferromagnets, it has been predicted1 that spin and charge are entangled, meaning that any change in the spin texture modifies the charge distribution. As a direct consequence of this entanglement, magnons should carry an electric dipole moment. Here we report evidence of this electric dipole moment in a graphene quantum Hall ferromagnet2,3 using a Mach–Zehnder interferometer. As magnons propagate across the insulating bulk, their electric dipole moment modifies the Aharonov–Bohm flux through the interferometer, affecting both phase and visibility of the interference pattern. In particular, we relate the phase shift to the sign of this electric dipole moment and the loss of visibility to the flux of emitted magnons, and we show that the magnon emission is a Poissonian process. Finally, we probe the emission energy threshold of the magnons for transient states, between ν = 0 and ν = 1, and link them to the emergence of the gapless mode predicted in the canted-antiferromagnetic phase at charge neutrality4,5. The ability to couple the spin degree of freedom to an electrostatic potential is a property of quantum Hall ferromagnets that could be promising for spintronics. Propagating spin waves known as magnons are expected to carry a dipole moment in the quantum Hall regime. Now, this moment has been detected, demonstrating that the degrees of freedom of spin and charge are entangled in quantum Hall magnons.

Magnons enable transferring a magnetic moment or spin over macroscopic distance. In quantum Hall ferromagnet, it has been predicted in the early 90s that spin and charges are entangled, meaning that any change of the spin texture modifies the charge distribution. As a direct consequence of this entanglement, magnons carry an electric dipole moment. Here we report the first evidence of the existence of this electric dipole moment in a graphene quantum Hall ferromagnet using a Mach-Zehnder interferometer as a quantum sensor. By propagating towards the interferometer through an insulating bulk, the magnon electric dipole moment modifies the Aharonov-Bohm flux through the interferometer, changing both its phase and its visibility. In particular, we relate the phase shift to the sign of this electric dipole moment, and the exponential loss of visibility to the flux of emitted magnons. Finally, we probe the emission energy threshold of the magnons close to filling factor v=1. Approaching v=0, we observe that the emission energy threshold diminishes towards zero, which might be linked to the existence of gapless mode in the canted-antiferromagnetic (CAF) phase at v=0. The detection and manipulation of magnons based on their electric dipole open the field for a new type of coherent magnon quantum circuits that will be electrostatically controlled.

This paper studies the Cramér-Rao bound (CRB) for burst-mode transmission synchronization of Single-Sideband Frequency Shift Keying (SSB-FSK). Based on the CRB computations of burst-mode CPM, for conventional double sided schemes, it was shown that it is possible to obtain an optimum training sequence that minimizes the CRBs simultaneously for the joint estimation of symbol timing, frequency offset, and carrier phase. However, due to the SSB-FSK non-antipodal alphabet, it is impossible to use the same optimum sequence to minimize the CRBs for all parameters simultaneously. Meanwhile, in this paper, we propose a new general training sequence that can minimize the sum of all CRBs for any binary SSB-FSK. The derived results can be helpful for data-aided (DA) synchronization of SSB-FSK modulation.

The recent realization of coherent single-electron sources in ballistic conductors let us envision performing time-resolved electronic interferometry experiments analogous to quantum optics experiments.One could eventually use propagating electronic excitations as flying qubits. However an important missing brick is the single-shot electron detection which would enable a complete quantum information operation with flying qubits. Here, we propose and discuss the design of a single charge detector able to achieve in-flight detection of electron flying qubits. Its sub-electron sensitivity would allow the detection of the fractionally charged flying anyons of the Fractional Quantum Hall Effect and would enable the detection of anyonic statistics using coincidence measurements.

In this paper, we calculate the Cramer-Rao bound (CRB) for single side band continuous phase modulation signals (SSB-FSK). The CRB is useful to design an optimum preamble sequence to jointly estimate the frequency offset, symbol timing, and carrier phase. The goal is to find preamble sequences that minimize the CRBs of all estimated parameters. The results provide some useful preambles, which can be added to data packets for synchronization in burst-mode SSB-FSK transmissions.

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted Josephson relation f(J) = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck's constant. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) on voltage V when irradiating contacts at microwaves frequency f(J). The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons.

The recent realization of single electron sources let us envision performing electron quantum optics experiments, where electrons can be viewed as flying qubits propagating in a ballistic conductor. To date, all electron sources operate in a periodic electron injection mode leading to energy spectrum singularities in various physical observables which sometimes hide the bare nature of physical effects. To go beyond this, we propose a spread-spectrum approach where electron flying qubits are injected in a non-periodic manner following a pseudorandom binary bit pattern. Extending the Floquet scattering theory approach from periodic to spread-spectrum drive, the shot noise of pseudorandom binary sequences of single electron injection can be calculated for leviton and non-leviton sources. Our new approach allows us to disentangle the physics of the manipulated excitations from that of the injection protocol. In particular, the spread spectrum approach is shown to provide a better knowledge of electronic Hong Ou Mandel correlations and to clarify the nature of the pulse train coherence and the role of the dynamical orthogonality catastrophe for non-integer charge injection.