The strongly attractive Fermi gas in the BCS-BEC crossover is efficiently described in terms of coupled fermions and fermion pairs, or molecules. We compute the spectral functions of both fermions and pairs in the normal state near the superfluid transition using a Keldysh formulation in real frequency. The mutual influence between fermions and pairs is captured by solving the self-consistent Luttinger-Ward equations: These include both the damping of fermions by scattering off dressed pairs and the decay of pair states by dissociation into two dressed fermions. The pair spectra encode contact correlations between fermions and form the basis for computing dynamical response functions and transport properties.

Recently, a method has been proposed to detect the rotation of a ring Bose-Einstein condensate, in situ, in real-time, and with minimal destruction by using a cavity driven with optical fields carrying orbital angular momentum [Phys. Rev. Lett. 127, 113601 (2021)]. This method is sensitive to the magnitude of the condensate winding number but not its sign. In the present work, we consider simulations of the rotation of the angular lattice formed by the optical fields and show that the resulting cavity transmission spectra are sensitive to the sign of the condensate winding number. We demonstrate the minimally destructive technique on persistent current rotational eigenstates, counter-rotating superpositions, and a soliton singly or in collision with a second soliton. Conversely, we also investigate the sensitivity of the ring condensate, given knowledge of its winding number, to the rotation of the optical lattice. This characterizes the effectiveness of the optomechanical configuration as a laboratory rotation sensor. Our results are important to studies of rotating ring condensates used in atomtronics, superfluid hydrodynamics, simulation of topological defects and cosmological theories, interferometry using matter-wave solitons, and optomechanical sensing.

We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute nonorthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. In other words, regardless of the initial-state preparation, the total probability remains constant but may be distinct from unity. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities. In contrast, classical realizations can surpass this bound. The violation of quantum bounds stems from the inability of classical ontological models, specifically the set-theoretic representation of the hypergraph corresponding to the quantum observables' collections, to adhere to and explain the observed statistics.

We compute the complexity for the mixed-state density operator derived from a one-dimensional discrete-time quantum walk (DTQW). The complexity is computed using a two-qubit quantum circuit obtained from canonically purifying the mixed state. We demonstrate that the Nielson complexity for the unitary evolution oscillates around a mean circuit depth of $k$. Further, the complexity of the stepwise evolution operator grows cumulatively and linearly with the steps. From a quantum circuit perspective, this implies a succession of circuits of (near) constant depth to be applied to reach the final state.

Measurements map the value of a target observable onto a meter shift, resulting in a meter readout that combines the initial statistics of the meter state with the quantum statistics of the target observable. Even in the limit of weak measurement interactions, some information about the fluctuations of the target observable can be extracted from the change in the readout fluctuations caused by the measurement interaction. Here, we apply the Heisenberg picture to analyze the changes in the meter readout statistics caused by sufficiently weak measurement interactions, including the effects of nonlinearities in the meter response. When additional information is obtained in a subsequent measurement of the system, the meter fluctuations are modified based on the postselected statistics of the target observable. In addition, our analysis reveals a direct modification of the meter fluctuations due to the dependence of the postselection probability on the dynamics induced by the meter in the measurement interaction. We point out that the quantum formalism makes it difficult to distinguish this dynamic term from the physical fluctuations of the target observable and stress the importance of distinguishing between genuine conditional fluctuations of the target observable and the dynamic pseudovariance associated with the measurement back-action.

The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed-matter physics to high-energy physics because of its nonperturbative behavior. Here we analyze the adiabatic dynamics in two-level systems and multilevel systems using exact WKB analysis, which is one of the nonperturbative analysis methods. As a result, we obtain a formula for the transition probability, which is similar to the known formula in the two-level system. Although nonperturbative analysis in the adiabatic limit has rarely been studied for multilevel systems, we show that the same analysis can be applied and also provide a concrete example. The results will serve as a basis for the application of exact WKB analysis in various fields of physics.

We investigate the steady-state charging process of a single-cell quantum battery embedded in an $N$-cell star network of qubits, each interacting with a fermion reservoir, collectively and individually in equilibrium and nonequilibrium scenarios, respectively. We find an optimal steady-state charging in both scenarios, which grows monotonically with the reservoirs' chemical potential and chemical potential difference, where the high base temperature of the reservoirs has a destructive role in all parameter regimes. We indicate that regardless of the strength of the nonequilibrium condition, the high base chemical potential of the battery's corresponding reservoir can significantly enhance the charging process. On the other hand, a weak-coupling strength can strongly suppress the charging. Consequently, our results could counteract the detrimental effects of self-discharging and provide valuable guidelines for enhancing the stable charging of open quantum batteries in the absence of an external charging field.

We revisit the celebrated Hellmann-Feynman theorem (HFT) in the parity-time $\left(\mathcal{PT}\right)$ invariant non-Hermitian quantum physics framework. We derive a modified version of HFT by changing the definition of inner product and explicitly show that it holds good for both $\mathcal{PT}$ broken and unbroken phases and even at the exceptional point of the theory. The derivation is extremely general and works for even the $\mathcal{PT}$ noninvariant Hamiltonian. We consider several examples of discrete and continuum variable systems to test our results. We find that, if the eigenvalue goes through a real-to-complex transition as a function of the Hermiticity breaking parameter, both sides of the modified HFT expression diverge at that point. If that point turns out to be an EP of the $\mathcal{PT}$-invariant quantum theory, then one also sees the divergence at EP. Moreover, we have also demonstrated that using the modified HFT can give rise to a potential numerical advantage for computing the expectation value of many-body operators for interacting many-body Hamiltonian. Finally, we also derive a generalized virial theorem for non-Hermitian systems using the modified HFT, which potentially can be tested in experiments.

When should a given operational phenomenology be deemed to admit of a classical explanation? When it can be realized in a generalized-noncontextual ontological model. The case for answering the question in this fashion has been made in many previous works and motivates research on the notion of generalized noncontextuality. Many criticisms and concerns have been raised, however, regarding the definition of this notion and of the possibility of testing it experimentally. In this work, we respond to some of the most common of these objections. One such objection is that the existence of a classical record of which laboratory procedure was actually performed in each run of an experiment implies that the operational equivalence relations that are a necessary ingredient of any proof of the failure of noncontextuality do not hold, and consequently that conclusions of nonclassicality based on these equivalences are mistaken. We explain why this concern is unfounded. Our response affords the opportunity for us to clarify certain facts about generalized noncontextuality, such as the possibility of having proofs of its failure based on a consideration of the subsystem structure of composite systems. Similarly, through our responses to each of the other objections, we elucidate some under-appreciated facts about the notion of generalized noncontextuality and experimental tests thereof.

In a practical continuous-variable quantum key distribution (CVQKD) system, the optical amplifier can be used to improve the performance of the system by compensating for the imperfections of the detectors. However, the eavesdropper Eve can actively utilize a reverse external magnetic field to deteriorate the performance of the optical amplifier, which may affect the practical security of the system. In this paper, we investigate the practical security of a CVQKD system with an optical amplifier under the effect of the reverse external magnetic field. Based on the investigation of the parameter estimation under the above influence, we find that the evaluation of the secret key rate may be overestimated, which will open a security loophole for Eve to successfully launch an intercept-resend attack in the practical CVQKD system with an optical amplifier. In order to close this security loophole, we can monitor the reverse external magnetic field or change the type of the optical isolator to make the secret key rate of the system evaluated exactly.

In pure-state tomography, the concept of unique determinedness (UD), the ability to uniquely determine pure states from measurement results, is crucial. This study presents a variational approach to examining UD, offering a robust solution to the challenges associated with the construction and certification of UD measurement schemes. We put forward an effective algorithm that minimizes a specially defined loss function, enabling the differentiation between UD and non-UD measurement schemes. This leads to the discovery of numerous optimal pure-state Pauli measurement schemes across a variety of dimensions. Additionally, we discern an alignment between uniquely determined among pure states and uniquely determined among all states in qubit systems when utilizing Pauli measurements, underscoring its intrinsic robustness under pure-state recovery. We further interpret the physical meaning of our loss function, bolstered by a theoretical framework. Our study not only propels the understanding of UD in quantum state tomography forward, but also delivers valuable practical insights for experimental applications, highlighting the need for a balanced approach between mathematical optimality and experimental pragmatism.

In recent work, Akers et al. [arXiv:2306.06163] proved that the entanglement of purification $E_p(A:B)$ is bounded below by half of the $q$-Rényi reflected entropy $S_R^{\left(q\right)}(A:B)$ for all $q\ge 2$, showing that $E_p(A:B)=\frac{1}{2}{S}_R^{\left(q\right)}(A:B)$ for a class of random tensor-network states. Naturally, the authors raise the question of whether a similar bound holds at $q=1$. Our work answers that question in the negative by finding explicit counterexamples, which we arrive at through numerical optimization. Nevertheless, this result does not preclude the possibility that restricted sets of states, such as conformal field theory states with semiclassical gravity duals, could obey the bound in question.

Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure states is solved. For mixed states, however, the verification of local unitary equivalence is still a challenging problem. In this paper, based on the coefficient matrices of generalized Bloch representations of quantum states, we find a variety of local unitary invariants for arbitrary-dimensional bipartite quantum states. These invariants are operational and can be used as necessary conditions for verifying the local unitary equivalence of two quantum states. Furthermore, we extend the construction to the arbitrary-dimensional multipartite case. We finally apply these invariants to estimate concurrence, a vital entanglement measure, showing the practicability of local unitary invariants in characterizing entanglement.

Preparation of bosonic and general cavity quantum states usually relies on using open-loop control to reach a desired target state. In this work, a measurement-based feedback approach is used instead, exploiting the nonlinearity of weak measurements alongside a coherent drive to prepare these states. The extension of previous work on Lyapunov-based control is shown to fail for this task. This prompts for a different approach, and reinforcement learning (RL) is resorted to here for this purpose. With such an approach, cavity-eigenstate superpositions can be prepared with fidelities over $98\%$ using only the measurements backaction as the nonlinearity, while naturally incorporating detection of cavity photon jumps. Two different RL frameworks are analyzed: an off-policy approach recently introduced called truncated quantile critic (TQC) and the on-policy method commonly used in quantum control, namely proximal policy optimization. It is shown that TQC performs better at reaching higher target state fidelity preparation.

The problem of finding the resource-free, closest local unitary, to any bipartite unitary gate $U$ is addressed. Previously discussed as a measure of nonlocality, the distance $K_D\left(U\right)$ to the nearest product unitary has implications for circuit complexity and related quantities. Dual unitaries, currently of great interest in models of complex quantum many-body systems, are shown to have a preferred role as these are maximally and equally away from the set of local unitaries. This is proved here for the case of qubits, and we present strong numerical and analytical evidence that it is true in general. An analytical evaluation of $K_D\left(U\right)$ is presented for general two-qubit gates. For arbitrary local dimensions, that $K_D\left(U\right)$ is largest for dual unitaries is substantiated by its analytical evaluations for an important family of dual-unitary and for certain nondual gates. A closely allied result concerns for any bipartite unitary the existence of a pair of maximally entangled states that it connects. We give efficient numerical algorithms to find such states and to find $K_D\left(U\right)$ in general.

The classical homotopy optimization approach has the potential to deal with highly nonlinear landscapes, such as the energy landscape of quantum approximate optimization algorithm (QAOA) problems. Following this motivation, we introduce Hamiltonian-oriented homotopy QAOA (HOHo-QAOA), a heuristic method for combinatorial optimization using QAOA, based on classical homotopy optimization. The method consists of a homotopy map that produces an optimization problem for each value of the interpolating parameter. Therefore, HOHo-QAOA decomposes the optimization of QAOA into several loops, each using a mixture of the mixer and the objective Hamiltonian for cost function evaluation. Furthermore, we conclude that the HOHo-QAOA improves the search for low-energy states in the nonlinear energy landscape and outperforms other variants of QAOA.

Qudit, a high-dimensional quantum system, can provide a larger Hilbert space, and it has been shown that the larger Hilbert space has remarkable advantages over the smaller one in quantum information processing. However, it is a great challenge to realize the high-fidelity quantum gates with qudits. Here we theoretically propose and experimentally demonstrate the four-dimensional quantum gates (including the generalized Pauli $X_4$ gate, Pauli $Z_4$ gate, and all of their integer powers) with optical qudits based on the polarization-spatial degree of freedom of the single photon. Furthermore, we also realize the polarization-controlled eight-dimensional controlled-$X_4$ gate and all of its integer powers. The experimental results achieve both the ultrahigh average gate fidelity $99.73\%$ and efficiency $99.47\%$, which are above the error threshold for fault-tolerant quantum computation. Our work paves the way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.

The nonadiabatic holonomic quantum computation (NHQC) has received great attention for decades, however, there are many challenges to its implementation in experiments. To further shorten the evolution time is the first challenge to be conquered to realize high-fidelity quantum gates in NHQC. In this paper, we propose a controlled two-qubit model in Rydberg atoms to realize nonadiabatic holonomic quantum gates, where the evolution time is extremely decreased and the influences of several kinds of noises are minimized by utilizing the time-optimal-control technique on the target atom. In addition, we can construct arbitrary geometric gates by selecting the appropriate parameters in our model. Furthermore, numerical simulations for the $\mathrm{C}-T$ gate and $\mathrm{C}-\sqrt{H}$ gate based on the master equation show that the fidelities of geometric gates obtained in our model are still very high even though noises are considered, which demonstrates the robustness of our protocol. It is worth noting that the controlled two-qubit model may pave the way to realize fault-tolerant quantum computation in the future.

Enantiodetection is an important and challenging task across natural sciences. The cyclic three-level models of chiral molecules provided possibilities to obtain the ultimate limit of the enantioselectivities in purely electric dipole effects, yielding an emerging frontier in enantiodetection. However, the generated enantioselectivities were usually severely reduced in the strong decoherence region, failing most of the related chiroptical methods. Here, we propose enantioselective switches of molecular responses by well designing the electromagnetic fields based on the dissipative cyclic three-level model of chiral molecules and provide a chiroptical method of enantiodetection. In our switches, the steady-state responses are turned on for the selected enantiomer and simultaneously turned off for its mirror image, which corresponds to the ultimate limit of enantioselectivities. The switches can survive in the strong decoherence regions, and so does the suggested chiroptical method of enantiodetection. Our results give more insight into answering whether the enantioselective responses of light based on the cyclic three-level model can survive in the strong decoherence region and thus have a potential impact on further research.