QUROPE Quantum Information Processing and Communication in Europe

We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask: what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with an instantaneous reset to a specified set of reset configurations taking place with a probability that depends on the current configuration of the system at the instant of reset? Analyzing the protocol in the framework of the so-called tight-binding model describing the hopping of a quantum particle to nearest-neighbour sites in a one-dimensional open lattice, we obtain analytical results for the probability of finding the particle on the different sites of the lattice. We explore a variety of dynamical scenarios, including the one in which the resetting time intervals are sampled from an exponential as well as from a power-law distribution, and a set-up that includes a Floquet-type Hamiltonian involving an external periodic forcing. Under exponential resetting, and in both presence and absence of the external forcing, the system relaxes to a stationary state characterized by localization of the particle around the reset sites. The choice of the reset sites plays a defining role in dictating the relative probability of finding the particle at the reset sites as well as in determining the overall spatial profile of the site-occupation probability. Indeed, a simple choice can be engineered that makes the spatial profile highly asymmetric even when the bare dynamics does not involve the effect of any bias. Furthermore, analyzing the case of power-law resetting serves to demonstrate that the attainment of the stationary state in this quantum problem is not always evident and depends crucially on whether the distribution of reset time intervals has a finite or an infinite mean.

High time-bandwidth product signal and idler pulses comprised of independent identically distributed two-mode squeezed vacuum (TMSV) states are readily produced by spontaneous parametric downconversion. These pulses are virtually unique among entangled states in that they offer quantum performance advantages -- over their best classical-state competitors -- in scenarios whose loss and noise break their initial entanglement. Broadband TMSV states' quantum advantage derives from its signal and idler having a strongly nonclassical phase-sensitive cross correlation, which leads to information bearing signatures in lossy, noisy scenarios stronger than what can be obtained from classical-state systems of the same transmitted energy. Previous broadband TMSV receiver architectures focused on converting phase-sensitive cross correlation into phase-insensitive cross correlation, which can be measured in second-order interference. In general, however, these receivers fail to deliver broadband TMSV states' full quantum advantage, even if they are implemented with ideal equipment. This paper introduces the correlation-to-displacement receiver -- a new architecture comprised of a correlation-to-displacement converter, a programmable mode selector, and a coherent-state information extractor -- that can be configured to achieve quantum optimal performance in known sensing and communication protocols for which broadband TMSV provides quantum advantage that is robust against entanglement-breaking loss and noise.

We consider the hypothetical quantum network case where Alice wishes to transmit one qubit of information (specifically a pure quantum state) to $M$ parties, where $M$ is some large number. The remote receivers locally perform single qubit quantum state tomography on the transmitted qubits in order to compute the quantum state within some error rate (dependent on the tomography technique and number of qubits used). We show that with the use of an intermediate optimal symmetric universal quantum cloning machine (between Alice and the remote receivers) as a repeater-type node in a hypothetical quantum network, Alice can send significantly fewer qubits compared to direct transmission of the message qubits to each of the $M$ remote receivers. This is possible due to two properties of quantum cloning. The first being that single qubit quantum clones retain the same angle, in the Bloch sphere representation, as the initial quantum state. This means that if the mixed state of the quantum clone can be computed to high enough accuracy, the pure quantum state can be computed by extrapolating that vector to the surface of the Bloch sphere. The second property is that the state overlap of approximate quantum clones, with respect to the original pure quantum state, quickly converges (specifically for $1 \rightarrow M$ the limit of the fidelity as M goes to infinity is $\frac{2}{3}$). This means that Alice can prepare a constant number of qubits (which are then passed through the quantum cloning machine) in order to achieve a desired error rate, if $M$ is large enough. Combined, these two properties mean that for large $M$, Alice can prepare orders of magnitude fewer qubits in order to achieve the same single qubit transmission accuracy compared to the naive direct qubit transmission approach.

The precise positioning of dopants in semiconductors using scanning tunneling microscopes has led to the development of planar dopant-based devices, also known as $\delta$-layers, facilitating the exploration of new concepts in classical and quantum computing. Recently it have been shown that two distinct conductivity regimes (low- and high- bias regimes) exist in $\delta$-layer tunnel junctions due to the presence of quasi-discrete and continuous states in the conduction band of $\delta$-layer systems. Furthermore, discrete charged impurities in the tunnel junction region significantly influence the tunneling rates in $\delta$-layer tunnel junctions. Here we demonstrate that zero-charge impurities, or electrical dipoles, present in the tunnel junction region can also significantly alter the tunneling rate, depending, however, on the specific conductivity regime and orientation and moment of the dipole. In the low-bias regime with high-resistance tunneling mode dipole impurities of nearly all orientations and moments can alter the current, indicating the extreme sensitivity of the tunnel current to the slightest imperfection in the tunnel gap. In the high-bias regime with low-resistivity only dipole defects with high moment and orientated in the direction perpendicular to the electron tunneling direction can significantly affect the current, thus making this conductivity regime significantly less prone to the influence of dipole defects with low-moment or dipoles oriented along the propagation direction.

Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of systems displaying topological order including, in particular, their anyon excitations. Here, we investigate systems that lie outside this common purview, and present a rich class of models exhibiting topological orders with distance-dependent interacting anyons. As we illustrate, in some instances, the gapped lowest-energy excitations are comprised of anyons that densely cover the entire system. This leads to behaviors not typically described by topological quantum field theories. We examine these models by performing dualities to systems displaying conventional (i.e., Landau) orders. Our approach enables a general method for mapping generic Landau-type theories to dual models with topological order of the same spatial dimension. The low-energy subspaces of our models can be made more resilient to thermal effects than those of surface codes.

We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of sub-ensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and determine the impact of finite size effects, inhomogeneous couplings between the spin and motional degrees of freedom and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.

We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the Hamiltonian of interest and collecting specific time-series measurements to estimate its spectrum. We demonstrate the advantage of our technique over currently used classical statistical sampling methods. We showcase our approach by experimentally estimating the spectral decomposition of a 2-qubit Heisenberg Hamiltonian on an IBM Quantum backend. For this purpose, we develop a hardware-efficient decomposition that controls $n$-qubit Pauli rotations against the physically closest qubit alongside expressing two-qubit rotations in terms of the native entangling interaction. This substantially reduced the accumulation of errors from noisy two-qubit operations in time evolution simulation protocols. We conclude by discussing the potential impact of our work and the future directions of research it opens.

The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We prove that the quantum acceleration is upper bounded by the fluctuation in the derivative of the Hamiltonian. This leads to a universal quantum acceleration limit (QAL) which answers the question: What is the minimum time required for a quantum system to be accelerated from arbitrary initial state to final state? We illustrate the quantum acceleration limit for a two-level quantum system and show that the bound is indeed tight. This notion can have important applications in adiabatic quantum computing, quantum control and quantum thermodynamics.

Within the self-gravitating Bose-Einstein condensate (BEC) model of dark matter (DM), we argue that the axionlike self-interaction of ultralight bosons ensures the existence of both rarefied and dense phases in the DM halo core of (dwarf) galaxies. In fact, this stems from two independent solutions of the Gross-Pitaevskii equation corresponding to the same model parameters. For a small number of particles, this structure disappears along with the gravitational interaction, and the Gross-Pitaevskii equation reduces to the stationary sine-Gordon equation, the one-dimensional antikink solution of which mimics a single-phase DM radial distribution in the halo core. Quantum mechanically, this solution corresponds to a zero-energy bound state of two particles in a closed scattering channel formed by the domain-wall potential with a finite asymptotics. To produce a two-particle composite with low positive energy and a finite lifetime, we appeal to the resonant transition of one asymptotically free particle of a pair from an open channel (with a model scattering potential) to the closed channel. Using the Feshbach resonance concept, the problem of two-channel quantum mechanics is solved in the presence of a small external influence which couples the two channels, and an analytical solution is obtained in the first approximation. Analyzing the dependence of scattering data on interaction parameters, we reveal a long-lived two-particle composite (dimer) possessing a lifetime of millions of years. This result is rather surprising and supposes important implications of dimers' being involved in forming large DM structures. It is shown that the dimers' appearance is related with the regime of infinite scattering length due to resonance. The revealed dependence of the DM scattering length $a$ on the parameters of interactions can theoretically justify variation of $a$ in the DM dominated galaxies.

We provide a group theory approach to coherent states describing quantum space-time and its properties. This provides a relativistic framework for the metric of a Riemmanian space with bosonic and fermionic coordinates, its continuum and discrete states, and a kind of {\it"quantum optics"} for the space-time. {\bf New} results of this paper are: (i) The space-time is described as a physical coherent state of the complete covering of the SL(2C) group, eg the Metaplectic group Mp(n). (ii) (The discrete structure arises from its two irreducible: $\textit{even}$ $(2n)$ and $\textit{odd}$ $(2n\;+\;1)\;$ representations, ($n = 1,\, 2, \,3\,...$ ), spanning the complete Hilbert space $\mathcal{H} = \mathcal{H}_{odd}\oplus \mathcal{H}_{even}$. Such a global or {\it complete} covering guarantees the CPT symmetry and unitarity. Large $n$ yields the classical and continuum manifold, as it must be. (iii) The coherent and squeezed states and Wigner functions of quantum-space-time for black holes and de Sitter, and (iv) for the quantum space-imaginary time (instantons), black holes in particular. They encompass the semiclassical space-time behaviour plus high quantum phase oscillations, and notably account for the classical-quantum gravity duality and trans-Planckian domain. The Planck scale consistently corresponds to the coherent state eigenvalue $\alpha = 0$ (and to the $n = 0$ level in the discrete representation). It is remarkable the power of coherent states in describing both continuum and discrete space-time. The quantum space-time description is {\it regular}, there is no any space-time singularity here, as it must be.

Single-mode optical fibres exhibit a small but non-negligible birefringence that induces random polarisation rotations during light propagation. In classical interferometry these rotations give rise to polarisation-induced fading of the interferometric visibility, and in fibre-based polarimetric sensors as well as quantum optics experiments they scramble the information encoded in the polarisation state. Correcting these undesired rotations is consequently an important part of many experiments and applications employing optical fibres. In this Lab Note we review an efficient method for fully compensating fibre polarisation rotations for general input states. This method was not originally devised by us, but does to the best of our knowledge not appear in the literature, and our interactions with the community have indicated that it is not well known.

Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction. A variety of decoders have been proposed for QLDPC codes and many of them utilize belief propagation (BP) decoding in some fashion. However, the use of BP decoding for degenerate QLDPC codes is known to face issues with convergence. These issues are commonly attributed to short cycles in the Tanner graph and multiple syndrome-matching error patterns due to code degeneracy. Although various methods have been proposed to mitigate the non-convergence issue, such as BP with ordered statistics decoding (BP-OSD) and BP with stabilizer inactivation (BP-SI), achieving better performance with lower complexity remains an active area of research. In this work, we propose to decode QLDPC codes with BP guided decimation (BPGD), which has been previously studied for constraint satisfaction and lossy compression problems. The decimation process is applicable to both binary BP and quaternary BP and involves sequentially freezing the value of the most reliable qubits to encourage BP convergence. Despite its simplicity, we find that BPGD significantly reduces BP failures due to non-convergence while maintaining a low probability of error given convergence, achieving performance on par with BP-OSD and BP-SI. To better understand how and why BPGD improves performance, we discuss several interpretations of BPGD and their connection to BP syndrome decoding.

Non-Hermitian (NH) physics has a close relationship with open and dissipative systems, attracting attentions increasingly. The conventional entropy based on the normalized probability distribution or density matrix is successful when describing the isolated system, but not always appropriate for the case of open systems. We develop a new approach using the generalized non-Hermitian entropy based on non-normalized density matrices to investigate the information dynamics of PT, anti-PT, and anyonic-PT symmetric systems. Our approach reveals three distinguished patterns of information dynamics in different areas of the parameter space of anti-PT and anyonic-PT symmetric Hamiltonians, respectively, which are three-fold degenerate and distorted when using the conventional entropy or trace distance adopted in previous works. According to our analysis and mathematical demonstration, it is the normalization of the non-normalized density matrices of the NH systems that leads to the three-fold degeneracy, as it causes the loss of information about the total probability flow between the NH system and the environment. Our approach using the generalized NH entropy and the non-normalized density matrices keeps all the nonunitary information of the NH systems, so that it can properly characterize the dynamical properties of the systems, avoiding the degeneracy of the entropy dynamics patterns.

Yttrium iron garnet (YIG) magnonics has sparked extensive research interests toward harnessing magnons (quasiparticles of collective spin excitation) for signal processing. In particular, YIG magnonics-based hybrid systems exhibit great potentials for quantum information science because of their wide frequency tunability and excellent compatibility with other platforms. However, the broad application and scalability of thin-film YIG devices in the quantum regime has been severely limited due to the substantial microwave loss in the host substrate for YIG, gadolinium gallium garnet (GGG), at cryogenic temperatures. In this study, we demonstrate that substrate-free YIG thin films can be obtained by introducing the controlled spalling and layer transfer technology to YIG/GGG samples. Our approach is validated by measuring a hybrid device consisting of a superconducting resonator and a spalled YIG film, which gives a strong coupling feature indicating the good coherence of our system. This advancement paves the way for enhanced on-chip integration and the scalability of YIG-based quantum devices.

In this habilitation thesis, I briefly present my work at Imperial College London on trapping atomic clouds in micro-pyramids fabricated on silicon chips, which led to the fabrication of an on-chip integrated atom source. Next, I describe the research carried out at the Laboratoire de Physique des Lasers in the SAI group. Our experiments demonstrated the temperature dependence of near-field Casimir-Polder interactions due to thermal excitation of surface waves, thus advancing our understanding of the dielectric properties of matter and the quantum vacuum that surrounds it. I also present spectroscopic experiments with atomic vapors confined in nanostructures (nano-sphere opals) aiming at the fabrication of miniature frequency references. Finally, I explore the possibility of performing spectroscopic experiments on molecular gases close to surfaces.

The role of Beam Splitters (BS) is crucial for quantum physics as it reveals the statistical behavior of quantum mechanical particles (quantons) and some of the fundamental quantum phenomena such as quantum superposition and randomness. Here, we investigate the use of BS and Phase Retarders (P) in combination and emphasize the importance of BS-P-BS systems for emerging quantum technologies. We demonstrate that the detection probabilities are equivalent to the spin measurement probabilities in analog setups. Then, by extending the discussion to spatially correlated two-quanton systems, we construct a suitable basis for analysis of other quantum mechanical processes that seem to have common origins. Last, we propose a new experimental setup for testing Bell-CHSH inequalities with spatially correlated two-quanton BS-P-BS systems by introducing topological phases.

For the paradigmatic three-disk scattering system, we confirm a recent conjecture for open chaotic systems, which claims that resonance states are composed of two factors. In particular, we demonstrate that one factor is given by universal exponentially distributed intensity fluctuations. The other factor, supposed to be a classical density depending on the lifetime of the resonance state, is found to be very well described by a classical construction. Furthermore, ray-segment scars, recently observed in dielectric cavities, dominate every resonance state at small wavelengths also in the three-disk scattering system. We introduce a new numerical method for computing resonances, which allows for going much further into the semiclassical limit. As a consequence we are able to confirm the fractal Weyl law over a correspondingly large range.

Non-local quantum computation (NLQC) is a cheating strategy for position-verification schemes, and has appeared in the context of the AdS/CFT correspondence. Here, we connect NLQC to the wider context of information theoretic cryptography by relating it to a number of other cryptographic primitives. We show one special case of NLQC, known as $f$-routing, is equivalent to the quantum analogue of the conditional disclosure of secrets (CDS) primitive, where by equivalent we mean that a protocol for one task gives a protocol for the other with only small overhead in resource costs. We further consider another special case of position verification, which we call coherent function evaluation (CFE), and show CFE protocols induce similarly efficient protocols for the private simultaneous message passing (PSM) scenario. By relating position-verification to these cryptographic primitives, a number of results in the cryptography literature give new implications for NLQC, and vice versa. These include the first sub-exponential upper bounds on the worst case cost of $f$-routing of $2^{O(\sqrt{n\log n})}$ entanglement, the first example of an efficient $f$-routing strategy for a problem believed to be outside $P/poly$, linear lower bounds on entanglement for CDS in the quantum setting, linear lower bounds on communication cost of CFE, and efficient protocols for CDS in the quantum setting for functions that can be computed with quantum circuits of low $T$ depth.

Using a general-order many-body Green's-function method for molecules, we numerically illustrate several pathological behaviors of the Feynman--Dyson diagrammatic perturbation expansion of one-particle many-body Green's functions as electron propagators. (i) The perturbation expansion of the frequency-dependent self-energy is not convergent at the exact self-energy in many frequency domains. (ii) An odd-perturbation-order self-energy has a qualitatively wrong shape and, as a result, most satellite roots of the Dyson equation with it are complex and nonphysical. (iii) The Dyson equation with an even-order self-energy has an exponentially increasing number of roots as the perturbation order is raised, which quickly exceeds the correct number of roots. (iv) Infinite partial summation of diagrams by vertex or edge modification exacerbates these problems. Not only does the nonconvergence render higher-order perturbation theories useless for satellite roots, but it also calls into question the validity of their combined use with the ans\"{a}tze requiring the knowledge of all poles and residues. Such ans\"{a}tze include the Galitskii--Migdal identity, self-consistent Green's-function methods, Luttinger--Ward functional, and some models of the algebraic diagrammatic construction.

Under suitable experimental conditions collective spin-wave excitations, magnons, form a Bose-Einstein condensate (BEC) where the spins precess with a globally coherent phase. Bose-Einstein condensation of magnons has been reported in a few systems, including superfluid phases of $^3$He, solid state systems such as Yttrium-iron-garnet (YIG) films, and cold atomic gases. Among these systems, the superfluid phases of $^3$He provide a nearly ideal test bench for coherent magnon physics owing to experimentally proven spin superfluidity, the long lifetime of the magnon condensate, and the versatility of the accessible phenomena. We first briefly recap the properties of the different magnon BEC systems, with focus on superfluid $^3$He. The main body of this review summarizes recent advances in application of magnon BEC as a laboratory to study basic physical phenomena connecting to diverse areas from particle physics and cosmology to new phases of condensed matter. This line of research complements the ongoing efforts to utilize magnon BECs as probes and components for potentially room-temperature quantum devices. In conclusion, we provide a roadmap for future directions in the field of applications of magnon BEC to fundamental research.