Quantum Physics (quant-ph)

Abstract: We consider the time-dependent transverse field Ising chain with time-periodic perturbations. Without perturbations, this model is one of the famous models that obeys the scaling in the adiabatic limit predicted by the quantum Kibble-Zurek mechanism (QKZM). However, it is known that when oscillations are added to the system, the non-perturbative contribution becomes larger and the scaling may break down even if the perturbation is small. Therefore, we analytically analyze the density of defects in the model and discuss how much the oscillations affect the scaling. As a result, although the non-perturbative contribution does not become zero in the adiabatic limit, the scaling does not change from the prediction of the QKZM. This indicates that the QKZM is robust to the perturbations.

Abstract: We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $\alpha$-$z$ R\'enyi relative entropy of magic. This allows us to identify a continuous set of magic monotones which are additive for single-qubit states and obtain much tighter upper bounds for magic state distillation. Moreover, we recover some already-known results and provide a complete picture of the additivity properties for single-qubit states for a wide class of monotones based on quantum relative entropies. We also derive a closed-form expression for all single-qubit states for the stabilizer fidelity and the generalized robustness of magic. Finally, we show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise, for which we give closed-form expressions.

Abstract: In this paper, we present a supervised learning technique that utilizes artificial neural networks to design new collective entanglement witnesses for two-qubit and qubit-qutrit systems. Machine-designed collective entanglement witnesses allow for continuous tuning of their sensitivity and selectivity. These witnesses are, thus, a conceptually novel instrument allowing to study the sensitivity vs. selectivity trade-off in entanglement detection. The chosen approach is also favored due to its high generality, lower number of required measurements compared to quantum tomography, and potential for superior performance with regards to other types of entanglement witnesses. Our findings could pave the way for the development of more efficient and accurate entanglement detection methods in complex quantum systems, especially considering realistic experimental imperfections.

Abstract: The nonlocal set has received wide attention over recent years. Shortly before, Li and Wang arXiv:2202.09034 proposed the concept of a locally stable set: the only possible orthogonality preserving measurement on each subsystem is trivial. Locally stable sets present stronger nonlocality than those sets that are just locally indistinguishable. In this work, we focus on the constructions of locally stable sets in multipartite quantum systems. First, two lemmas are put forward to prove that an orthogonality-preserving local measurement must be trivial. Then we present the constructions of locally stable sets with minimum cardinality in bipartite quantum systems $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ $(d\geq 3)$ and $\mathbb{C}^{d_{1}}\otimes \mathbb{C}^{d_{2}}$ $(3\leq d_{1}\leq d_{2})$. Moreover, for the multipartite quantum systems $(\mathbb{C}^{d})^{\otimes n}$ $(d\geq 2)$ and $\otimes^{n}_{i=1}\mathbb{C}^{d_{i}}$ $(3\leq d_{1}\leq d_{2}\leq\cdots\leq d_{n})$, we also obtain $d+1$ and $d_{n}+1$ locally stable orthogonal states respectively. Fortunately, our constructions reach the lower bound of the cardinality on the locally stable sets, which provides a positive and complete answer to an open problem raised in arXiv:2202.09034 .

Abstract: How to manage coherence as a continuous variable quantum resource is still an open question. We face this situation from the very definition of incoherent states in quadrature basis. We apply several measures of coherence for some physical states of light relative to a quadrature basis. We examine the action on the coherence of several transformations such as beam splittings and squeezing.

Abstract: In this Letter, a new approximate Quantum State Preparation (QSP) method is introduced, called the Walsh Series Loader (WSL). The WSL approximates quantum states defined by real-valued functions of single real variables with a depth independent of the number $n$ of qubits. The circuit depth is also $O(1/\sqrt{\epsilon})$, where $\epsilon$ is the precision of the approximation. The size is $O(n+1/\sqrt{\epsilon})$ and only one ancilla qubit is needed, giving an overall efficient algorithm with no exponential scaling. The protocol can be generalized to any complex-valued, multi-variate differentiable function. The Walsh Series Loader is so far the only method which prepares a quantum state with a circuit depth independent of the number of qubits.

Abstract: Squeezed states of the optical field were theoretically described in the early 1970s and first observed in the mid 1980s. The measured photon number of a squeezed state is correlated with the measured photon numbers of all other squeezed states of the same ensemble, providing sub-Poissonian statistics. Today all gravitational-wave observatories use squeezed light as the cost-efficient alternative to further scaling up the light power. This user application of quantum correlations was made possible through dedicated research and development of squeezed light between 2002 and 2010.

Abstract: We have proved new estimates for the coherent control errors of quantum circuits used in quantum computing. These estimates essentially take into account the commutator properties of the Hamiltonians and are based on the formulas of the commutator calculus.

Abstract: We present a barycentric decomposition for quantum instruments whose output space is finite-dimensional and input space is separable. As a special case, we obtain a barycentric decomposition for channels between such spaces and for normalized positive-operator-valued measures in separable Hilbert spaces. This extends the known results by Ali and Chiribella et al. on decompositions of quantum measurements, and formalises the fact that every instrument between finite-dimensional Hilbert spaces can be represented using only finite-outcome instruments.

Abstract: Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level connections between problems and quantum resources. It is argued here that new models are needed to achieve high-level algorithmic expressiveness that allow composable procedural abstractions to manifest, leading to the development of instructions in the sense usually understood in high-level programming languages. Doing so appears essential to the discovery of new quantum algorithms, and deeper understanding of how quantum resources compose into useful patterns, or \emph{quantum motifs}. To achieve this, stronger investment in the intersection between higher-algebra, mathematical physics and quantum science is required to cope with future challenges brought forth by \textit{very large quantum scale integration}.

Abstract: In this study, we introduce the concept of a quantum circuit autoencoder to compress and encode information within quantum circuits. Quantum circuit autoencoder also serves as a generalization of the quantum state autoencoder. Our first step involves presenting a protocol for the quantum circuit autoencoder and designing a variational quantum algorithm named QCAE that can implement it. We then explore the conditions necessary for lossless compression and establish an upper bound on the recovery fidelity of QCAE. Furthermore, we identify how the lossless condition enables us to construct a loss function and avoid the Barren Plateau problem. Following the classical autoencoder approach, we apply QCAE to dimension reduction and anomaly detection for quantum circuits. Finally, we evaluate the effectiveness of our proposed quantum circuit autoencoder through numerical simulations. Our results show that QCAE can efficiently compress and recover quantum circuits with high fidelity and identify circuit outliers precisely.

Abstract: Coherence plays an important role in quantum resource theory, which is strongly related with entanglement. Similar to the entanglement factorization law, we find the coherence factorization law of quantum states through fully and strictly incoherent operation (FSIO) channels. In order to quantify the full coherence of qudit states, we define G-coherence and convex roof of G-coherence, and prove that the G-coherence is a strong coherence monotone and the convex roof of G-coherence is a coherence measure under FSIO, respectively. Experimental verification of the coherence factorization law for qubits and qutrits under genuinely incoherent operations (GIOs) has been shown in [Photonics Research \textbf{10}, 2172 (2022)]. Actually, GIO is a special case of FSIO. We prove that coherence factorization law can be generalized under all possible FSIO channels for arbitrary qudit states.

Abstract: Discrimination of quantum states under local operations and classical communication (LOCC) is an intriguing question in the context of local retrieval of classical information, encoded in the multipartite quantum systems. All the local quantum state discrimination premises, considered so far, mimic a basic communication set-up, where the spatially separated decoding devices are independent of any additional input. Here, exploring a generalized communication scenario we introduce a framework for input-dependent local quantum state discrimination, which we call local random authentication (LRA). Referring to the term nonlocality, often used to indicate the impossibility of local state discrimination, we coin the term conditional nonlocality for the impossibility associated with the task LRA. We report that conditional nonlocality necessitates the presence of entangled states in the ensemble, a feature absent from erstwhile nonlocality arguments based on local state discrimination. Conversely, all the states in a complete basis set being entangled implies conditional nonlocality. However, the impossibility of LRA also exhibits more conditional nonlocality with less entanglement. The relation between the possibility of LRA and local state discrimination for sets of multipartite quantum states, both in the perfect and conclusive cases, has also been established. The results highlight a completely new aspect of the interplay between the security of information in a network and quantum entanglement under the LOCC paradigm.

Abstract: As a quantum resource, quantum coherence plays an important role in modern physics. Many coherence measures and their relations with entanglement have been proposed, and the dynamics of entanglement has been experimentally studied. However, the knowledge of general results for coherence dynamics in open systems is limited. Here we propose a coherence factorization law, which describes the evolution of coherence passing through any noisy channels characterized by genuinely incoherent operations. We use photons to implement the quantum operations and experimentally verify the law for qubits and qutrits. Our work is a step toward the understanding of the evolution of coherence when the system interacts with the environment, and will boost the study of more general laws of coherence.

Abstract: The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. GRAPE is gradient search method based on exact expressions for gradient of the control objective. It has been applied to coherently controlled closed and open quantum systems. In this work, we adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. In our case, the tailored or engineered environment acts on the system as control via it time-dependent decoherence rates $\gamma_k(t)$ or, equivalently, via it spectral density of the environment $n_\omega(t)$. To develop GRAPE approach for this problem, we compute gradient of various objectives for general N-level open quantum systems both for piecewise class of control. The case of a single qubit is considered in details and solved analytically. For this case, an explicit analytical expression for evolution and objective gradient is obtained via diagonalization of a $3\times 3$ matrix determining the system's dynamics in the Bloch ball. The diagonalization is obtained by solving a cubic equation via Cardano's method. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem and its complexity is estimated.

Abstract: We examine a variational class of generalized Ramsey protocols incorporating two one-axis-twisting (OAT) operations, with one performed prior to the phase imprint and the other following it. Within this framework, we optimize the axes of the signal imprint and the OAT interactions, as well as the direction of the final projective measurement. We differentiate between protocols that exhibit symmetric or anti-symmetric dependencies of the spin projection signal on the measured phase. Our findings reveal that the quantum Fisher information, which sets the bounds for sensitivity achievable with a given one-axis-twisted input state, can be maximized within our variational protocol class for almost all initial twisting strengths. By encompassing numerous protocols previously documented in the literature, our approach establishes a unified framework for Ramsey echo protocols involving OAT states and measurements.

Abstract: Arguments by Sorkin arXiv:gr-qc/9302018 and Borsten, Jubb, and Kells arXiv:1912.06141 establish that a natural extension of quantum measurement theory from non-relativistic quantum mechanics to relativistic quantum theory leads to the unacceptable consequence that expectation values in one region depend on which non-selective measurement is performed in a spacelike separated region. Sorkin labels such scenarios "impossible measurements". We explicitly present these arguments as a no-go result with the logical form of a reductio argument and investigate the consequences for measurement in quantum field theory (QFT). Sorkin-type impossible measurement scenarios clearly illustrate the moral that Microcausality is not by itself sufficient to rule out superluminal signalling in relativistic quantum theories that use L\"uders' rule. We review three different approaches to formulating an account of measurement for QFT and analyze their responses to the "impossible measurements" problem. Two of the approaches are: a measurement theory based on detector models proposed in Polo-G\'omez, Garay, and Mart\'in-Mart\'Inez arXiv:2108.02793 and a measurement framework for algebraic QFT proposed in Fewster and Verch arXiv:1810.06512. Of particular interest for foundations of QFT is that they share common features that may hold general morals about how to represent measurement in QFT. These morals are about the role that dynamics plays in eliminating "impossible measurements", the abandonment of the operational interpretation of local algebras as representing possible operations carried out in a region, and the interpretation of state update rules. Finally, we examine the form that the "impossible measurements" problem takes in histories-based approaches and we discuss the remaining challenges.

Abstract: Scalability presents a central platform challenge for the components of current quantum network implementations that can be addressed by microfabrication techniques. We demonstrate a proof-of-principle realization of a high-bandwidth quantum memory in a warm alkali atom ensemble in a MEMS vapor cell compatible with wafer-scale fabrication. By applying an external tesla-order magnetic field, we explore a novel ground-state memory scheme in the hyperfine Paschen-Back regime, where individual optical transitions can be addressed in a Doppler-broadened medium. Working on the $^{87}$Rb D$_2$ line, where deterministic quantum dot single-photon sources are available, we demonstrate bandwidth-matching with 100s of MHz broad light pulses keeping such sources in mind. For a storage time of 80 ns we measure an end-to-end efficiency of $\eta_{e2e}^{\text{80ns}} = 3.12(17)\%$, corresponding to an internal efficiency of $\eta_{\text{int}}^{\text{0ns}} = 24(3)\%$, while achieving a signal-to-noise ratio of $\text{SNR} = 7.9(8)$ with coherent pulses at the single-photon level.

Abstract: We report spectroscopy experiments of rubidium vapor in a high magnetic field under conditions of electromagnetically induced transparency (EIT) and optical pumping. The 1.1 T static magnetic field decouples nuclear and electronic spins and shifts each magnetic state via the Zeeman effect, allowing us to resolve individual optical transitions of the D$_2$ line in a Doppler-broadened medium. By varying the control laser power driving one leg of a spectrally isolated lambda system we tune the vapor from the EIT regime to conditions of Autler-Townes line splitting (ATS). The resulting spectra conform to simple three-level models demonstrating the effective simplification of the energetic structure. Further, we quantify the viability of state preparation via optical pumping on nuclear spin-forbidden transitions. We conclude that the ``cleanliness'' of this system greatly enhances the capabilities of quantum control in hot vapor, offering advantages in a broad variety of quantum applications plagued by spurious light-matter interaction processes, such as atomic quantum memories for light.

Abstract: Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask.

Abstract: According to the Kibble-Zurek mechanism, there is a universal power-law relationship between the defect density and the quench rate during a slow linear quench through a critical point. It is generally accepted that a fast quench results in a deviation from the Kibble-Zurek scaling law and leads to the formation of a saturated plateau in the defect density. Our focus is on the transitions of quench dynamics as quench rates vary from slow to very fast limits. Through an in-depth analysis of the transverse Ising chain, we have identified a pre-saturated regime that lies between the saturated and Kibble-Zurek regimes. As we approach the transition point from the saturated to pre-saturated regimes, we notice a change in scaling laws and, with an increase in the initial transverse field, a shrinking of the saturated regime until it disappears. During another transition from the Kibble-Zurek to pre-saturated regimes, we observe an attenuation of the dephasing effect and a change in the behavior of the kink-kink correlation function from a Gaussian decay to an exponential decay.

Abstract: Practical quantum networks require interfacing quantum memories with existing channels and systems that operate in the telecom band. Here we demonstrate low-noise, bidirectional quantum frequency conversion that enables a solid-state quantum memory to directly interface with telecom-band systems. In particular, we demonstrate conversion of visible-band single photons emitted from a silicon-vacancy (SiV) center in diamond to the telecom O-band, maintaining low noise ($g^2(0)<0.1$) and high indistinguishability ($V=89\pm8\%$). We further demonstrate the utility of this system for quantum networking by converting telecom-band time-bin pulses, sent across a lossy and noisy 50 km deployed fiber link, to the visible band and mapping their quantum states onto a diamond quantum memory with fidelity $\mathcal{F}=87\pm 2.5 \% $. These results demonstrate the viability of SiV quantum memories integrated with telecom-band systems for scalable quantum networking applications.

Abstract: The Hidden Quantum Markov Model(HQMM) shows tremendous potential for analyzing time-series data and studying stochastic processes in the quantum world due to its high accuracy and better efficiency compared to the classical hidden Markov model. Here, we proposed the project to realize the hidden quantum Markov process using the conditional master equation, which includes a fine balance condition and better reflects the relationships among the inner states of quantum system. The experimental results indicate that our model has better performance and robust than previous models for time-series data. Most importantly, by taking the quantum transport system as an example, we establish the relations between the quantum conditional master equation and the HQMM, and propose a new learning algorithm to determine the parameter-solving in HQMM. Our findings provide obvious evidence that the quantum transport system can be deemed a physical embodiment of HQMM.

Abstract: In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of $\hat{\rho}_{\mathbf{\theta}}$ can be produced rapidly (e.g., in optics), the information-extraction bottleneck can stem from high post-processing costs or detector saturation. In these regimes, it is desirable to compress the information encoded in $\hat{\rho}_{\mathbf{\theta}} \, ^{\otimes n}$ into $m<n$ copies of a postselected state: ${\hat{\rho}_{\mathbf{\theta}}^{\text{ps}}} \,^{\otimes m}$. Remarkably, recent works have shown that, in the absence of noise, compression can be lossless, for $m/n$ arbitrarily small. Here, we fully characterize the family of filters that enable lossless compression. Further, we study the effect of noise on quantum-metrological information amplification. Motivated by experiments, we consider a popular family of filters, which we show is optimal for qubit probes. Further, we show that, for the optimal filter in this family, compression is still lossless if noise acts after the filter. However, in the presence of depolarizing noise before filtering, compression is lossy. In both cases, information-extraction can be implemented significantly better than simply discarding a constant fraction of the states, even in the presence of strong noise.

Abstract: The maximum-entropy principle (Max-Ent) is a valuable and extensively used tool in statistical mechanics and quantum information theory. It provides a method for inferring the state of a system by utilizing a reduced set of parameters associated with measurable quantities. However, the computational cost of employing Max-Ent projections in simulations of quantum many-body systems is a significant drawback, primarily due to the computational cost of evaluating these projections. In this work, a novel approach for estimating Max-Ent projections is proposed. The approach involves replacing the expensive Max-Ent induced local geometry, represented by the Kubo-Mori-Bogoliubov (KMB) scalar product, with a less computationally demanding geometry. Specifically, a new local geometry is defined in terms of the quantum analog of the covariance scalar product for classical random variables. Relations between induced distances and projections for both products are explored. Connections with standard variational and dynamical Mean-Field approaches are discussed. The effectiveness of the approach is calibrated and illustrated by its application to the dynamic of excitations in a XX Heisenberg spin-$\frac{1}{2}$ chain model.

Abstract: The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.