In Sperling et al. [Phys. Rev. Lett. 118, 163602 (2017)], we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multiphoton states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data.

We show that an entangled traveling photon-phonon pair can be generated in a resonator-waveguide structure via optomechanical interaction. We employ the “backward Heisenberg picture” approach to write an analytic expression for the output quantum state, from which the generation efficiency and the entanglement of the photon-phonon pair are calculated. We find that the photon-phonon entanglement can be manipulated by adjusting the spectral width of the input pulse.

We study cross-relaxation resonances between differently oriented groups of nitrogen-vacancy (NV) centers at small external magnetic fields. These resonances are observed using resonant optical pumping on the NV-center zero phonon line. We suggest a magnetometry protocol that is based on measuring the positions of cross-relaxation resonances on the fluorescence scan. This protocol does not require microwave radiation and can be used to find all components of the unknown magnetic field vector. A room-temperature variant of the protocol with off-resonant optical pumping is also briefly discussed.

The group-velocity-led optical event horizon (OEH) in optical fibers provides a convenient way to efficiently control a weak dispersive pulse by a comparatively strong solitonic pulse. State-of-the-art experiments demonstrating OEH make use of two different light sources, which increases the system complexity and cost. Here, we propose an elegant and cost-effective approach to observe the OEH through intermodal nonlinear interaction between azimuthally symmetric ${\text{LP}}_{01}$ and ${\text{LP}}_{02}$ modes of a specially designed triple-clad multimode fiber through only a single pump. The simultaneous control over dispersion and the walk off of ${\text{LP}}_{01}$ and ${\text{LP}}_{02}$ modes of the designed fiber pave the way for the OEH interaction. The ${\text{LP}}_{02}$ mode possesses anomalous dispersion, while the ${\text{LP}}_{01}$ mode exhibits normal dispersion over the wavelength range of interest. Depending upon the location of the input pump wavelength, the ${\text{LP}}_{02}$ soliton can reflect a weak copropagating ${\text{LP}}_{01}$ dispersive pulse, which possesses the same carrier wavelength as the soliton. The findings of this work might be useful for all-optical switching and also for the optical transistor action, where the increased feasibility is obtained by the fact that the proposed approach does not require separate input wavelengths for the soliton and the dispersive pulse. Moreover, a tunable pump source can be used to observe either a redshift or a blueshift in the dispersive pulse.

We analyze a measurement scheme that allows determination of the Berry curvature and the topological Chern number of a Hamiltonian with parameters exploring a two-dimensional closed manifold. Our method uses continuous monitoring of the gradient of the Hamiltonian with respect to one parameter during a quasiadiabatic quench of the other. Measurement backaction leads to disturbance of the system dynamics, but we show that this can be compensated by a feedback Hamiltonian. As an example, we analyze the implementation with a superconducting qubit subject to time-varying, near-resonant microwave fields, equivalent to a spin-1/2 particle in a magnetic field.

The photon blockade (PB) effect in emitter-cavity systems depends on the anharmonicity of the ladder of dressed energy eigenstates. The recent developments in color center photonics are leading toward experimental demonstrations of multiemitter-cavity solid-state systems with an expanded set of energy levels compared to the traditionally studied single-emitter systems. We focus on the case of $N=2$ nonidentical quasiatoms strongly coupled to a nanocavity in the bad cavity regime (with parameters within reach of the color center systems), and discover three PB mechanisms: polaritonic, subradiant, and unconventional. The polaritonic PB, which is the conventional mechanism studied in single-emitter-cavity systems, also occurs at the polariton frequencies in multiemitter systems. The subradiant PB is a new interference effect owing to the inhomogeneous broadening of the emitters which results in a purer and a more robust single-photon emission than the polaritonic PB. The unconventional PB in the modeled system corresponds to the suppression of the single- and two-photon correlation statistics and the enhancement of the three-photon correlation statistic. Using the effective Hamiltonian approach, we unravel the origin and the time-domain evolution of these phenomena.

We demonstrate the emergence of an entire flat band with no complex component embedded in dispersive bands at the exceptional point of a $\mathcal{PT}$-symmetric photonic lattice. For this to occur, the gain and loss parameter effectively alters the size of the partial flat band windows and band gap of the photonic lattice simultaneously. The mode associated with the entire flat band is robust against changes in the system size and survives even at the edge of the lattice. Our proposal offers a route for controllable localization of light in non-Hermitian systems and a technique for measuring non-Hermiticity via localization.

We present an exhaustive numerical analysis of violations of local realism by families of multipartite quantum states. As an indicator of nonclassicality we employ the probability of violation for randomly sampled observables. Surprisingly, it rapidly increases with the number of parties or settings and even for relatively small values local realism is violated for almost all observables. We have observed this effect to be typical in the sense that it emerged for all investigated states including some with randomly drawn coefficients. We also present the probability of violation as a witness of genuine multipartite entanglement.

Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.

We study the nonequilibrium dynamics of two mechanical oscillators with general linear couplings to two uncorrelated thermal baths at temperatures $T_1$ and $T_2$, respectively. We obtain the complete solution of the Heisenberg-Langevin equations, which reveal a coherent mixing among the normal modes of the oscillators as a consequence of their off-diagonal couplings to the baths. Unique renormalization aspects resulting from this mixing are discussed. Diagonal and off-diagonal (coherence) correlation functions are obtained analytically in the case of strictly Ohmic baths with different couplings in the strong- and weak-coupling regimes. An asymptotic nonequilibrium stationary state emerges for which we obtain the complete expressions for the correlations and coherence. Remarkably, the coherence survives in the high-temperature, classical limit for $T_1\ne T_2$. This is a consequence of the coherence being determined by the difference of the bath correlation functions. In the case of vanishing detuning between the oscillator normal modes both coupling to one and the same bath, the coherence retains memory of the initial conditions at long times. An out-of-equilibrium setup with small detuning and large $|T_1-T_2|$ produces nonvanishing steady-state coherence in the high-temperature limit of the baths.

The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order $O\left({\partial }_t^2\right)$. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.

Quantum key distribution can be enhanced and extended if nonclassical single-photon states of light are used. We study a connection between the security of quantum key distribution and quantum non-Gaussianity of light arriving at the receiver's detection system after the propagation through a noisy quantum channel, being under full control of an eavesdropper performing general collective attacks. We show that while quantum nonclassicality exhibited by the light arriving at the receiver's station is a necessary indication of the security of the discrete-variable protocols, quantum non-Gaussianity can be a sufficient indication of their security. Therefore, checking for non-Gaussianity of this light by performing standard autocorrelation function measurement can be used for prior verification of the usability of prepare-and-measure schemes. It can play a similar role to the prior verification of the quantum correlations sufficient to violate Bell inequalities for entanglement-based protocols.

We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension 1, if an SPTO phase protects the identity gate, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation.

Blind quantum computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's input, output, and computation remain private. A desirable property for any BQC protocol is verification, whereby the client can verify with high probability whether the server has followed the instructions of the protocol or if there has been some deviation resulting in a corrupted output state. A verifiable BQC protocol can be viewed as an interactive proof system leading to consequences for complexity theory. We previously proposed [A. Broadbent, J. Fitzsimons, and E. Kashefi, in Proceedings of the 50th Annual Symposium on Foundations of Computer Science, Atlanta, 2009 (IEEE, Piscataway, 2009), p. 517] a universal and unconditionally secure BQC scheme where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. In this paper we extend that protocol with additional functionality allowing blind computational basis measurements, which we use to construct another verifiable BQC protocol based on a different class of resource states. We rigorously prove that the probability of failing to detect an incorrect output is exponentially small in a security parameter, while resource overhead remains polynomial in this parameter. This resource state allows entangling gates to be performed between arbitrary pairs of logical qubits with only constant overhead. This is a significant improvement on the original scheme, which required that all computations to be performed must first be put into a nearest-neighbor form, incurring linear overhead in the number of qubits. Such an improvement has important consequences for efficiency and fault-tolerance thresholds.

We prove quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well-known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control of the performance of generalized universal quantum cloning machines (UQCMs) on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a priori information in the context of cloning. For example, we can control the performance of an antisymmetric analog of the UQCM in recovering from the loss of $n-k$ fermionic particles.

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

We determine the cost of performing Shor's algorithm for integer factorization on a ternary quantum computer, using two natural models of universal fault-tolerant computing: (i) a model based on magic state distillation that assumes the availability of the ternary Clifford gates, projective measurements, classical control as its natural instrumentation set; (ii) a model based on a metaplectic topological quantum computer (MTQC). A natural choice to implement Shor's algorithm on a ternary quantum computer is to translate the entire arithmetic into a ternary form. However, it is also possible to emulate the standard binary version of the algorithm by encoding each qubit in a three-level system. We compare the two approaches and analyze the complexity of implementing Shor's period-finding function in the two models. We also highlight the fact that the cost of achieving universality through magic states in MTQC architecture is asymptotically lower than in generic ternary case.

Producing and maintaining entanglement reside at the heart of the optimal construction of quantum operations and are fundamental issues in the realization of universal quantum computation. We here introduce a setup of spin qubits that allows the geometric implementation of entangling gates between the register qubits with any arbitrary entangling power. We show this by demonstrating a circuit through a spin chain, which performs universal nonadiabatic holonomic two-qubit entanglers. The proposed gates are all electric and geometric, which would help to realize fast and robust entangling gates on spin qubits. This family of entangling gates contains gates that are as efficient as the cnot gate in quantum algorithms. We examine the robustness of the circuit to some extent.

We consider the quantum Rabi model with external time modulation of the atomic frequency, which can be employed to create excitations from the vacuum state of the electromagnetic field as a consequence of the dynamical Casimir effect. Excitations can also be systematically subtracted from the atom-field system by suitably adjusting the modulation frequency, in the so-called antidynamical Casimir effect (ADCE). We evaluate the quantum thermodynamical work and show that a realistic out-of-equilibrium finite-time protocol harnessing ADCE allows for work extraction from the system, whose amount can be much bigger than the modulation amplitude, $|W_{\mathrm{ADCE}}|\gg \hslash {\epsilon }_{\mathrm{\Omega }}$, in contrast to the case of very slow adiabatic modulations. We provide means to control work extraction in state-of-the-art experimental scenarios, where precise frequency adjustments or complete system isolation may be difficult to attain.