In a standard bipartite Einstein-Podolsky-Rosen (EPR) scenario, Alice and Bob share a system prepared in an entangled state and Alice performs local measurements. One possible generalization of this setup is to allow Bob to also locally process his subsystem. Then correlations generated in such generalized EPR scenarios are examples of nonsignaling bipartite resources, called assemblages, that can exhibit postquantum behavior, i.e., cannot be generated using solely quantum systems. There exist assemblages that, despite being postquantum resources, can only generate quantum correlations in bipartite Bell-type scenarios. Here we present a protocol for activation of postquantumness in bipartite generalized EPR scenarios such as the so-called Bob-with-input, measurement-device-independent, and channel EPR scenarios. By designing a protocol that involves distributing the assemblages in a larger network, we derive tailored Bell inequalities which can be violated beyond their quantum bound in this new setup. Our results show that in all of the above generalized scenarios, the postquantumness of the assemblages can be witnessed at the level of correlations they produce.

Fock states and their superpositions are exotic test beds for nonclassical physics and valuable resources for quantum technologies. We provide a simple protocol for the quantum measurement to generate an arbitrary Fock state and certain superposed Fock states from a coherent state of a target resonator, without any carefully tailored driving. This conditional protocol can be efficiently constructed by a sequence of joint free evolution of the resonator and an ancillary qubit, which are coupled via a Jaynes-Cummings interaction, and projective measurements on the qubit. By properly choosing the duration of each evolution-measurement cycle and the initial state of the resonator, we can generate a desired Fock state $|n\rangle$ and a superposed Fock state $\left(\right|0\rangle +|n\rangle )/\sqrt{2}, n\sim 10$, with a fidelity over $99\%$ in less than 30 measurements. Moreover, our protocol can be extended straightforwardly to the generation of a Bell-like state $\left(\right|00\rangle +|nn\rangle )/\sqrt{2}$ with multiple excitations in a double-resonator system. We also calculate the outcome fidelity and the success probability of our protocol in the presence of decoherence.

This work presents the problem of learning an unknown von Neumann measurement of dimension $d$ using indefinite causal structures. In the considered scenario, we have access to $N$ copies of the measurement. We use the formalism of process matrices to store information about the given measurement that later will be used to reproduce its best possible approximation. Our goal is to compute the maximum value of the average fidelity function $F_d\left(N\right)$ of our procedure. We prove that $F_d\left(N\right)=1-\mathrm{\Theta }\left(\frac{1}{N^2}\right)$ for arbitrary but fixed dimension $d$. Furthermore, we present the SDP program (semi-definite program) for computing $F_d\left(N\right)$. Basing on the numerical investigation, we show that for the qubit von Neumann measurements using indefinite causal learning structures provide better approximation than quantum networks, starting from $N\ge 3$.

We present a general condition to obtain subspaces that decay uniformly in a system governed by the Lindblad master equation and use them to perform error-mitigated quantum computation. The expectation values of dynamics encoded in such subspaces are unbiased estimators of noise-free expectation values. In analogy to the decoherence free subspaces which are left invariant by the action of Lindblad operators, we show that the uniformly decaying subspaces are left invariant (up to orthogonal terms) by the action of the dissipative part of the Lindblad equation. We apply our theory to a system of qubits and qudits undergoing relaxation with varying decay rates and show that such subspaces can be used to eliminate bias up to first-order variations in the decay rates without requiring full knowledge of noise. Since such a bias cannot be corrected through standard symmetry verification, our method can improve error mitigation in dual-rail qubits and, given partial knowledge of noise, can perform better than probabilistic error cancellation.

We consider a quantum system of three chainwise connected states $1\text{−}2\text{−}3$, in a $\mathrm{\Lambda }$ linkage pattern, in which the middle state is subjected to strong population decay. We show that this scenario can be used to create coherent superpositions between the two ground states. The idea is to deplete the population of the bright state formed by the two ground states 1 and 3 via the population loss channel. Then the surviving population is trapped in the dark state. The latter can be designed a priori, by selecting suitable couplings, to be equal to any desired coherent superposition of the ground states. In particular, for equal couplings on the $1\text{−}2$ and $2\text{−}3$ transitions, equal superposition between states 1 and 3 is created. Moreover, its phase can be controlled by the relative phase between the $1\text{−}2$ and $2\text{−}3$ fields. The present concept is an alternative to the slow adiabatic creation of coherent superpositions and may therefore be realized over short times, especially in the case where the middle state has a short life span. However, the price we pay for the fast evolution is associated with an overall 50% population loss. This issue can be removed in an experiment by using postselection. Interestingly, this physical scenario can be used to test the probabilistic interpretation of quantum mechanics in a very simple experiment. Indeed, if the probabilistic interpretation is correct and the decay from the middle state 2 is virtual (until measured), then the coherent superposition of states 1 and 3 is created. However, if the decay from state 2 actually occurs during the process, then there are two possibilities: Either state 2 decays and the population leaves the system completely, or state 2 does not decay and the population remains in the system. By suitably choosing the couplings we can make sure that in the latter case (no decay) the population returns to the initial state 1 with certainty. In both cases state 3 will end up with zero population. Therefore, by measuring the population of state 3 alone, we can find out if the probabilistic interpretation is correct (if its population is $\frac{1}{4}$) or not (if its population is 0).

Quantum information processing with neutral atoms relies on Rydberg excitation for entanglement generation. While the use of heavy divalent or open-shell elements, such as strontium or ytterbium, has benefits due to their optically active core and a variety of possible qubit encodings, their Rydberg structure is generally complex. For some isotopes in particular, hyperfine interactions are relevant even for highly excited electronic states. We employ multichannel quantum defect theory to infer the Rydberg structure of isotopes with nonzero nuclear spin and perform nonperturbative Rydberg-pair interaction calculations. We find that due to the high level density and sensitivities to external fields, experimental parameters must be precisely controlled. Specifically in ${}^{87}\mathrm{Sr}$, we study an intrinsic Förster resonance, unique to divalent atoms with hyperfine-split thresholds, which simultaneously provides line stability with respect to external field fluctuations and enhanced long-range interactions. Additionally, we provide parameters for pair states that can be effectively described by single-channel Rydberg series. The explored pair states provide exciting opportunities for applications in the blockade regime, as well as for more exotic long-range interactions such as largely flat, distance-independent potentials.

Pairs of entangled photons are important for applications in quantum nanophotonics, where their theoretical description must accommodate their bipartite character. Such character is shared at the other end of the intensity range by, for example, the two degenerate instances of the pump field involved in second-harmonic generation. The description and numerical simulation of the interaction of nanophotonic structures with bipartite states of light are challenging regardless of their intensity and have important technological applications. To address such a challenge, we develop here a theoretical and computational framework for studying the interaction of material structures with bipartite states of light. The theory of the framework rests on the symmetrized tensor product space of two copies of an electromagnetic Hilbert space. For the computational side, the convenient $T$-matrix method is extended to the tensor product space. When the response of the object to one part of the state is independent of the other part, the $T$ matrix for bipartite states is a simple function of the typical $T$ matrix of the single Hilbert space. Such a separable material response is relevant, for example, in the interaction of entangled biphoton states with nanostructures. Nonseparable operators are identified as adequate objects to fully integrate nonlinear effects such as sum-frequency generation or parametric down-conversion. As an example of application, we derive selection rules for second-order nonlinear processes in objects with rotational and/or mirror symmetries and verify them numerically in two different ${\mathrm{MoS}}_2$ clusters.

Color centers in diamond and silicon carbide, and molecular spins through a host matrix control are promising for nanoscale quantum sensing because they can be optically addressable, coherently controllable, and placed proximate to the targets. However, large transverse zero-field splitting (ZFS) is often inevitable due to their intrinsic symmetry and/or the high local strains of the host matrix. Although spin coherence can be extended due to magnetic noise-insensitive clock transitions at a vanishing magnetic field, the eigenstates of these sensors are not sensitive to weak magnetic signals in the linear order. We address this challenge by employing a combination of radio-frequency (rf) field driving along the NV orientation and microwave dynamic decoupling pulse sequences. Radio-frequency driving can effectively mitigate the transverse ZFS effect and enhance the NV center's sensitivity to ac magnetic field signals. This combination not only suppresses environmental noise but also enables quantum frequency mixing between the transverse ZFS and the signal. It also offers the potential to detect weak ac signals at intermediate and high frequencies with high resolution, a task difficult to achieve using conventional methods.

Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution.

Superresolution has been demonstrated to overcome the limitation of Rayleigh's criterion and achieve significant precision improvement in resolving the separation of two incoherent optical point sources. However, in recent years, it was found that, if the photon numbers of two incoherent optical sources are unknown, the precision of superresolution vanishes when the photon numbers are actually different. In this work, we first analyze in detail the estimation precision of the separation for two incoherent optical sources with the same point-spread functions and show that, when the two photon numbers are different but sufficiently close, the superresolution can still be realized but with different precisions. We find the condition on how close the photon numbers need to be to realize the superresolution and derive the precision of superresolution in different regimes of the photon number difference. We further consider the superresolution for two incoherent optical sources with different point-spread functions and show that the competition between the difference of photon numbers, the difference of point-spread functions, and the separation of source locations determines the precision of superresolution. The results exhibit precision limits distinct from that of two identical point-spread functions with equal photon numbers and extend the realizable regimes of quantum superresolution. Finally, the results are illustrated by Gaussian point-spread functions.

We employed the multiconfiguration Dirac-Hartree-Fock method to calculate the hyperfine magnetic dipole and electric quadrupole interaction constants $A$ and $B$ for the $5d6s{}^{3}D_{1,2,3}$, ${}^{1}D_2$ and $6s6p{}^{3}P_{1,2}^o$, ${}^{1}P_1^o$ states, as well as the isotope shift factors for transitions between these states and the ground state in ${\mathrm{Lu}}^{+}$. The effects of electron correlations, Breit interaction, and QED correction on these physical quantities were investigated using the active-space approach. By combining the experimentally measured hyperfine interaction constants $B$ with the theoretically calculated electric-field gradients produced by electrons at the nucleus, the nuclear electric quadrupole moment of ${}^{175}\mathrm{Lu}$ was re-evaluated as $Q\left({}^{175}\mathrm{Lu}\right)=3.53\left(17\right)\mathrm{b}$, which is very consistent with the recommended value $Q\left({}^{175}\mathrm{Lu}\right)=3.49\left(2\right)\mathrm{b}$ [Stone, At. Data Nucl. Data Tables 111–112, 1 (2016); Pyykkö, Mol. Phys. 116, 1328 (2018)]. The field shifts in the $6s^2{}^{1}S_0-5d6s{}^{3}D_{1,2,3},{}^{1}D_2$ and $6s^2{}^{1}S_0\text{−}6s6p{}^{3}P_{0,1,2}^o,{}^{1}P_1^o$ transitions are over an order of magnitude larger than the mass shifts, facilitating the deduction of changes in nuclear charge mean-square radii. Combining the experimentally measured isotope shift and theoretically calculated field shift factor of the $6s^2{}^{1}S_0-5d6s{}^{3}D_1$ transition, the difference of the mean-square charge radii of ${}^{175,176}\mathrm{Lu}$ was obtained as $\delta {\langle r^2\rangle }^{175,176}=0.0521{\mathrm{fm}}^2$, which is in reasonable agreement with the recommended value [Angeli and Marinova, At. Data Nucl. Data Tables 99, 69 (2013)]. Our results resolve the long-standing significant discrepancies in previous estimations.

As opposed to what is widely described in literature, quantum plasmon-polariton excitations are characterized by two families of creation and annihilation operators associated by continuity with the free electromagnetic field and the medium oscillators. In this paper, we elaborate the quantum plasmonics theory using the canonical quantization technique by means of the Lippmann-Schwinger equation: We derive (i) the polaritonic electromagnetic field, modified by the presence of a finite-size medium, expressed in terms of the classical Green function satisfying the Sommerfeld outgoing radiation condition, and (ii) the imaginary Green's function identity, which both complement the forms of bulk models used in literature. We prove the standard Purcell formula of a two-level quantum emitter, located near or inside the medium, emerging via a compensation of two terms in the respective expressions of the electric field and the imaginary Green's function identity, that are not present in a bulk configuration. These results provide a solid foundation for further developments with suitable physical interpretations of quantum nanotechnologies with dielectric or metallic structures in interaction with quantum emitters.

Topological lasers based on optical cavity arrays, such as the Su-Schrieffer-Heeger array, in active media were recently realized on various platforms. In all these studies the coupling coefficient between any adjacent sites of the lattice was positive. Consequently, the lasing mode featured an out-of-phase oscillation which is typically impractical for any application because it weakens the far-field intensity. This problem can be mitigated by altering the coupling signs along the array. However, implementing negative evanescent coupling in microrings, microdisks and micropillars is not possible using standard designs and fabrication processes. In this work, we design and experimentally implement a photonic crystal cavity array that consists of three sites where the sign of one coupling parameter is inverted, which enables the observation of an in-phase symmetry-protected zero mode. The photonic crystal array presented here utilizes the recently proposed “image-barrier” technique, in which the photonic barriers are copied at opposite sides of the array, which mitigates chain-termination effects and at the same time enables sign flip from one barrier to the adjacent one, resulting in “twisted coupling.” Consequently, the overall symmetry of the zero mode is inverted and becomes even, which is experimentally demonstrated. Our work opens the door for implementing a new generation of phase-locked topological laser arrays that oscillate in the same phase with enhanced far-field optical intensities.

Discrete-time quantum walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental physics, as some of them have a continuum limit converging to well-known physics partial differential equations, such as the Dirac or the Schrödinger equation. In this paper, we show how to recover the Dirac equation in $(3+1)$ dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved space-time. This also suggests an ordered scheme for propagating matter over a spin network, of interest in loop quantum gravity, where matter propagation has remained an open problem.

We investigate the performances of multiphoton anisotropic Dicke quantum battery (QB), which couples a finite number $N$ of identical and independent two-level systems (TLSs) to a unique cavity mode. Each transition of TLS is accompanied by the absorption or emission of $l$ photons from the cavity mode. In this model, the coupling constants of rotating and counterrotating wave terms are independent. Therefore, we utilize this interesting property to investigate the role of counterrotating wave terms and find that the higher the proportion of counterrotating wave terms, the higher the average power. Moreover, it is shown that the charging process is progressively faster by increasing the coupling strength from the weak to the ultrastrong and deep strong coupling regime. In the deep strong regime, the anti-Tavis-Cummings (ATC) coupling can almost achieve the optimal energy storage in a short time, which can be used to realize the feasibility of QB. Furthermore, we also analyze the effects of multiphoton interaction and single-multiphoton mixing process on the battery performances.

We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant (EFT) quantum computers in the context of models of their implementations on a surface code architecture. We estimate the logical and physical resources required to use these protocols to calculate the ground-state energy of molecular hydrogen in a minimal basis with error below ${10}^{-3}$ atomic units, in the presence of depolarizing logical errors. Accounting for the overhead of rotation synthesis and magic state distillation, we find that the total $T$-gate counts do not vary significantly among the EFT QPE protocols at fixed state overlap. In addition to reducing the number of ancilla qubits and circuit depth, the noise robustness of the EFT protocols can be leveraged to reduce resource requirements below those of textbook QPE, realizing an approximately 300-fold reduction in aggregate computational volume in some cases. We also compare resource requirements for QPE on Trotterized time evolution and qubitized walk operators, for this same minimal exemplar. We estimate the costs of these two approaches to be comparable, with the Trotter approach requiring slightly fewer physical qubits and the qubitized approach requiring slightly fewer code cycles. Even so, our estimates are well beyond the scale of existing early fault-tolerance demonstrations.

This paper investigates the dynamics of a two-level system coupled to a super-Ohmic boson bath, which is the so-called driven spin-boson model. Using the polaron transformation we derive the Bloch vector of a master equation where the bar tunneling parameter is used as the basis for a perturbation expansion. Our method is based on the canonical quantization provided by the Bloch-Redfield formalism. We apply quantum optimal control theory to the realization of a quantum $Z$ gate and also the coherent destruction of tunneling. To solve our optimal control problem, we use the techniques of automatic differentiation as an alternative to Pontryagin's minimum principle. The latter is less straightforward since the master equation is complex.

We propose a quantum-enhanced metrology protocol known as partially concurrent twisting and sensing (PCTS) to effectively utilize time for high-precision sensing. In contrast to the traditional approach of separated twisting and sensing (STS), we concurrently execute twisting and sensing at the outset. Here, we explore one-axis twisting (OAT) over a short evolution period to induce spin squeezing, which has been used in several quantum-enhanced metrology. In particular for tiny estimated parameter, we analytically give the measurement precision of PCTS and demonstrate its metrological advantages compared with STS. Especially for modest particle number and OAT interaction strength, PCTS makes better use of entanglement generation time and achieves a larger metrological gain within the same total time. We estimate that our PCTS may offer up to 2 dB of metrological advantage over STS in realistic experiments with Bose condensed atoms or trapped ions. Although the measurement precision of PCTS may diminish with increasing estimated parameters, we can employ two hybrid classical-PCTS compensation techniques to facilitate high-precision measurements across a wide dynamic range. Furthermore, our approach eliminates the need to switch the estimated field, thereby reducing experimental demands and offering extensive application potential in atomic clocks and magnetometers.