We provide an efficient method for the calculation of high-gain, twin-beam generation in waveguides. Equations of motion are derived that naturally accommodate photon generation via spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM), and also include the effects of both self-phase modulation (SPM) of the pump, and of cross-phase modulation (XPM) of the twin beams by the pump. The equations we solve involve fields that evolve in space and are labelled by a frequency. We provide a proof that these fields satisfy bonafide commutation relations, and that in the distant past and future they reduce to standard time-evolving Heisenberg operators. Finally, we consider the example of high-gain SPDC in a waveguide with a flat nonlinearity profile, for which our approach provides an explicit solution that requires only a single matrix exponentiation.

In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as compact quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance. More recently I have dealt with corresponding statements in the literature about vector bundles on spheres and matrix algebras. But physicists want, even more, to treat structures on spheres (and other spaces) such as Dirac operators, Yang-Mills functionals, etc., and they want to approximate these by corresponding structures on matrix algebras. In preparation for understanding what the Dirac operators should be, we determine here what the corresponding "cotangent bundles" should be for the matrix algebras, since it is on them that a "Riemannian metric" must be defined, which is then the information needed to determine a Dirac operator. (In the physics literature there are at least 3 inequivalent suggestions for the Dirac operators.)

Auger recombination is a non-radiative process, where the recombination energy of an electron-hole pair is transferred to a third charge carrier. It is a common effect in colloidal quantum dots that quenches the radiative emission with an Auger recombination time below nanoseconds. In self-assembled QDs, the Auger recombination has been observed with a much longer recombination time in the order of microseconds. Here, we use two-color laser excitation on the exciton and trion transition in resonance fluorescence on a single self-assembled quantum dot to monitor in real-time every quantum event of the Auger process. Full counting statistics on the random telegraph signal give access to the cumulants and demonstrate the tunability of the Fano factor from a Poissonian to a sub-Poissonian distribution by Auger-mediated electron emission from the dot. Therefore, the Auger process can be used to tune optically the charge carrier occupation of the dot by the incident laser intensity; independently from the electron tunneling from the reservoir by the gate voltage. Our findings are not only highly relevant for the understanding of the Auger process, it also demonstrates the perspective of the Auger effect for controlling precisely the charge state in a quantum system by optical means.

We present a framework to control and track the observables of a general solid state system driven by an incident laser field. The main result is a non-linear equation of motion for tracking an observable, together with a constraint on the size of expectations which may be reproduced via tracking. Among other applications, this model provides a potential route to the design of laser fields which cause photo-induced superconductivity in materials above their critical temperature. As a first test, the strategy is used to make the expectation value of the current conform to an arbitrary function under a range of model parameters. Additionally, using two reference spectra for materials in the conducting and insulating regimes respectively, the tracking algorithm is used to make each material mimic the optical spectrum of the other.

We propose the utilization of the IBM Quantum Experience quantum computing system to simulate different scenarios involving common hybrid quantum system components, the Nitrogen Vacancy Centre (NV centre) and the Flux Qubit. We perform a series of the simulation experiments and demonstrate properties of a virtual hybrid system, including its spin relaxation rate and state coherence. In correspondence with experimental investigations we look at the scalability of such systems and show that increasing the number of coupled NV centres decreases the coherence time. We also establish the main error rate as a function of the number of control pulses in evaluating the fidelity of the four qubit virtual circuit with the simulator. Our results show that the virtual system can attain decoherence and fidelity values comparable to what has been reported for experimental investigations of similar physical hybrid systems, observing a coherence time at 0.35 s for a single NV centre qubit and fidelity in the range of 0.82. The work thus establishes an effective simulation test protocol for different technologies to test and analyze them before experimental investigations or as a supplementary measure.

In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.

We introduce an approximate description of an $N$-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of $N$. We show, in fact, that the error in the estimation of the observables' expectation values decreases as the inverse of the square root of the number of the system's identical preparations and increases, at most, linearly in a suitably defined, $N$-independent, seminorm of the observables. Building the approximate description of the $N$-qubit state only requires repetitions of single-qubit rotations followed by single-qubit measurements and can be considered for implementation on today's Noisy Intermediate-Scale Quantum (NISQ) computers. The access to the expectation values of all observables for a given state leads to an efficient variational method for the determination of the minimum eigenvalue of an observable. The method represents one example of the practical significance of the approximate description of the $N$-qubit state. We conclude by briefly discussing extensions to generative modelling and with fermionic operators.

We propose quantum subroutines for the simplex method that avoid classical computation of the basis inverse. For a well-conditioned $m \times n$ constraint matrix with at most $d_c$ nonzero elements per column, at most $d$ nonzero elements per column or row of the basis, and optimality tolerance $\epsilon$, we show that pricing can be performed in time $\tilde{O}(\frac{1}{\epsilon}\sqrt{n}(d_c n + d^2 m))$, where the $\tilde{O}$ notation hides polylogarithmic factors. If the ratio $n/m$ is larger than a certain threshold, the running time of the quantum subroutine can be reduced to $\tilde{O}(\frac{1}{\epsilon}d \sqrt{d_c} n \sqrt{m})$. Classically, pricing would require $O(d_c^{0.7} m^{1.9} + m^{2 + o(1)} + d_c n)$ in the worst case using the fastest known algorithm for sparse matrix multiplication. We also show that the ratio test can be performed in time $\tilde{O}(\frac{t}{\delta} d^2 m^{1.5})$, where $t, \delta$ determine a feasibility tolerance; classically, this requires $O(m^2)$ in the worst case. For well-conditioned sparse problems the quantum subroutines scale better in $m$ and $n$, and may therefore have a worst-case asymptotic advantage. An important feature of our paper is that this asymptotic speedup does not depend on the data being available in some "quantum form": the input of our quantum subroutines is the natural classical description of the problem, and the output is the index of the variables that should leave or enter the basis.

The manipulation of quantum "resources" such as entanglement and coherence lies at the heart of quantum advantages and technologies. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are inevitably contaminated by noises and thus often lost their power or become unreliable for direct usage. Here we derive fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource. Remarkably, it is impossible to achieve perfect resource purification, even probabilistically. Our theorems indicate strong limits on the efficiency of distillation, a widely-used type of resource purification routine that underpins many key applications of quantum information science. In particular, we present explicit lower bounds on the resource cost of magic state distillation, a leading scheme for realizing scalable fault-tolerant quantum computation.

The geometric phase acquired by an electron in a one-dimensional periodic lattice due to weak electric perturbation is found and referred to as the Pancharatnam-Zak phase. The underlying mathematical structure responsible for this phase is unveiled. As opposed to the well-known Zak phase, the Pancharatnam-Zak phase is a gauge invariant observable phase, and correctly characterizes the energy bands of the lattice. We demonstrate the gauge invariance of the Pancharatnam-Zak phase in two celebrated models displaying topological phases. A filled band generalization of this geometric phase is constructed and is observed to be sensitive to the Fermi-Dirac statistics of the band electrons. The measurement of the single-particle Pancharatnam-Zak phase in individual topological phases, as well as the statistical contribution in its many-particle generalization, should be accessible in various controlled quantum experiments.

We develop a rigorous theoretical approach for analyzing inelastic scattering of photon pairs in arrays of two-level qubits embedded in a waveguide. Our analysis reveals strong enhancement of the scattering when the energy of incoming photons resonates with the double-excited subradiant states. We identify the role of different double-excited states in the scattering such as superradiant, subradiant, and twilight states, being a product of single-excitation bright and subradiant states. Importantly, the N-excitation subradiant states can be engineered only if the number of qubits exceeds 2N. Both the subradiant and twilight states can generate long-lived photon-photon correlations, paving the way to a storage and processing of quantum information.

The work distribution function for a non-relativistic, non-interacting quantum many-body system interacting with classical external sources is investigated. Exact expressions for the characteristic function corresponding to the work distribution function is obtained for arbitrary switching function and coupling functions. The many-body frequencies are assumed to be generally time-dependent in order to take into account the possibility of moving the boundaries of the system in a predefined process linking the characteristic function to the fluctuation-induced energies in confined geometries. Some limiting cases are considered and discussed.

We show how Cooper-pair-assisted transport, which describes the stimulated transport of electrons in the presence of Cooper-pairs, can be engineered and controlled with cold atoms, in regimes that are difficult to access for condensed matter systems. Our model is a channel connecting two cold atomic gases, and the mechanism to generate such a transport relies on the coupling of the channel to a molecular BEC, with diatomic molecules of fermionic atoms. Our results are obtained using a Floquet-Redfield master equation that accounts for an exact treatment of the interaction between atoms in the channel. We explore, in particular, the impact of the coupling to the BEC and the interaction between atoms in the junction on its transport properties, revealing non-trivial dependence of the produced particle current. We also study the effects of finite temperatures of the reservoirs and the robustness of the current against additional dissipation acting on the junction. Our work is experimentally relevant and has potential applications to dissipation engineering of transport with cold atoms, studies of thermoelectric effects, quantum heat engines, or Floquet Majorana fermions.

Apparatus for fluorescence-based single photon generation includes collection optics and various setups for characterization. This can have complexity when tweaking in one part changes the optimal alignment of everything. We suggest here a modular system, where each compartment is given the optimal alignment and has independent self-tests. Based on this concept, we built a stable and extendable system for single photon generations with fluorescence center in nano-flakes. The system has advantages of extending the number of single mode fiber output, which are connected to various external setups for analysis and reserved for practical uses as a photon source in radiometry. Another benefit is a high level of stability to preserve the optimal condition with the help of internal self-tests in each module. For demonstrations, we had a crystal-defect fluorescence center in hexagonal boron nitride nano-flake, and produced a single photon stream qualified by the single photon factor $g^{(2)}(0) = 0.25$ and the maximum count rate of $3 \times 10^5$ per second at a saturation point. Due to high stability, we prolonged a single photon stream over an hour with uniform count rates.

Contextuality is an indicator of non-classicality, and a resource for various quantum procedures. In this paper, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.

Author(s): A. Ferreri, V. Ansari, C. Silberhorn, and P. R. Sharapova

The two-photon Hong-Ou-Mandel (HOM) interference is a pure quantum effect which indicates the degree of indistinguishability of photons. The four-photon HOM interference exhibits richer dynamics in comparison to the two-photon interference and simultaneously is more sensitive to the input photon sta...

[Phys. Rev. A 100, 053829] Published Thu Nov 14, 2019

Author(s): A. A. Balakin, A. G. Litvak, and S. A. Skobelev

The propagation of laser pulses in multicore fibers (MCFs) made of a central core and an even number of cores located in a ring around it is studied. Approximate quasisoliton homogeneous solutions of the wave field in the MCF considered are found. The stability of the in-phase soliton distribution i...

[Phys. Rev. A 100, 053830] Published Thu Nov 14, 2019

Author(s): D. B. Horoshko, S. De Bièvre, G. Patera, and M. I. Kolobov

We introduce thermal-difference states (TDSs), a three-parameter family of single-mode non-Gaussian bosonic states whose density operator is a weighted difference of two thermal states. We show that the states of “heralded photons” generated via parametric down-conversion (PDC) are precisely those a...

[Phys. Rev. A 100, 053831] Published Thu Nov 14, 2019

Author(s): Kai Wang, Qin Wu, Ya-Fei Yu, and Zhi-Ming Zhang

It is shown that the Fizeau drag can cause nonreciprocity. We propose the use of a nanostructured ring cavity made of χ(2) nonlinear materials to achieve a nonreciprocal photon blockade (PB) through the Fizeau drag. Under the weak driving condition, we discuss the PB phenomena for the fundamental mo...

[Phys. Rev. A 100, 053832] Published Thu Nov 14, 2019

Author(s): Yahong Chen, Andreas Norrman, Sergey A. Ponomarenko, and Ari T. Friberg

We introduce a class of partially coherent surface plasmon polariton (SPP) fields carrying optical vortices, generated through a judicious superposition of planar SPPs with a prescribed initial phase distribution and arbitrary correlations at a metal-air interface. We explore the global degree of co...

[Phys. Rev. A 100, 053833] Published Thu Nov 14, 2019