Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements’ incompatibility, via backaction on the state. Mathematically, a weak value—a preselected and postselected expectation value—lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement’s ability to reconcile incompatible operations.

Quantifying the efficiency of random target search strategies is a key question of random walk theory, with applications in various fields. If many results do exist for recurrent processes, for which the probability of eventually finding a target in infinite space—so called hitting probability—is one, much less is known in the opposite case of transient processes, for which the hitting probability is strictly less than one. Here, we determine the universality classes of the large distance behavior of the hitting probability for general $d$-dimensional transient jump processes, which we show are parametrized by a transience exponent that is explicitly given.

The security of real-world quantum key distribution (QKD) critically depends on the number of data points the system can collect in a finite time interval. To date, state-of-the-art finite-key security analyses require block lengths in the order of ${10}^4\mathrm{bits}$ to obtain positive secret keys. This requirement, however, can be very difficult to achieve in practice, especially in the case of entanglement-based satellite QKD, where the overall channel loss can go up to 70 dB or more. Here, we provide an improved finite-key security analysis which reduces the block length requirement by 14% to 17% for standard channel and protocol settings. In practical terms, this reduction could save entanglement-based satellite QKD weeks of measurement time and resources, thereby bringing space-based QKD technology closer to reality. As an application, we use the improved analysis to show that the recently reported Micius QKD satellite is capable of generating positive secret keys with a ${10}^{-5}$ security level.

Symmetric informationally complete (SIC) positive operator valued measures (POVMs) are a class of quantum measurements which, in addition to being informationally complete, satisfy three conditions: (1) every POVM element is rank one, (2) the Hilbert-Schmidt inner product between any two distinct elements is constant, and (3) the trace of each element is constant. The third condition is often overlooked, since it may give the impression that it follows trivially from the second. We show that this condition cannot be removed, as it leads to two distinct values for the trace of an element of the POVM. This observation has led us to define a broader class of measurements which we call semi-SIC POVMs. In dimension two, we show that semi-SIC POVMs exist, and we construct the entire family. In higher dimensions, we characterize key properties and applications of semi-SIC POVMs, and note that the proof of their existence remains open.

We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates—or linear combinations thereof—using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their “round-trip” time) locks in at rational ratios $sT/r$ of the driving period $T$, where $s$, $r$ are coprime integers. Wave packets of different $s/r$ can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely ($s/r=1$) or over a long time ($s/r\ne 1$). Discrete time translation symmetry is manifestly broken for $s\ne 1$, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.

The interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of the Anderson transitions driven by non-Hermitian disorders for a three-dimensional (3D) Anderson model and 3D U(1) model, which belong to 3D class ${\mathrm{AI}}^{†}$ and 3D class A in the classification of non-Hermitian systems, respectively. Based on level statistics and finite-size scaling analysis, the critical exponent for the length scale is estimated as $\nu =0.99\pm 0.05$ for class ${\mathrm{AI}}^{†}$, and $\nu =1.09\pm 0.05$ for class A, both of which are clearly distinct from the critical exponents for 3D orthogonal and 3D unitary classes, respectively. In addition, spectral rigidity, level spacing distribution, and level spacing ratio distribution are studied. These critical behaviors strongly support that the non-Hermiticity changes the universality classes of the Anderson transitions.

Nonlocal games with advantageous quantum strategies give arguably the most fundamental demonstration of the power of quantum resources over their classical counterparts. Recently, certain multiplayer generalizations of nonlocal games have been used to prove unconditional separations between limited computational complexity classes of shallow-depth circuits. Here, we show advantageous strategies for these nonlocal games for generic ground states of one-dimensional symmetry-protected topological orders (SPTOs), when a discrete invariant of a SPTO known as a twist phase is nontrivial and $-1$. Our construction demonstrates that sufficiently large string order parameters of such SPTOs are indicative of globally constrained correlations useful for the unconditional computational separation.

We present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the tropical algebra defined on the semiring of $(\mathbb{R}\cup \{-\infty \},\oplus ,\odot )$. Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the ordinary algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes the computational power of graphical processing units (GPUs). For applications, we compute the exact ground state energy of Ising spin glasses on square lattice up to 1024 spins, on cubic lattice up to 216 spins, and on three regular random graphs up to 220 spins, on a single GPU; we obtain exact ground state energy of $\pm J$ Ising spin glass on the chimera graph of D-Wave quantum annealer of 512 qubits in less than 100 s and investigate the exact value of the residual entropy of $\pm J$ spin glasses on the chimera graph; finally, we investigate ground-state energy and entropy of three-state Potts glasses on square lattices up to size $18\times 18$. Our approach provides baselines and benchmarks for exact algorithms for spin glasses and combinatorial optimization problems, and for evaluating heuristic algorithms and mean-field theories.

In an effort to address integrability breaking in cold gas experiments, we extend the integrable hydrodynamics of the Lieb-Liniger model with two additional components representing the population of atoms in the first and second transverse excited states, thus enabling a description of quasi-1D condensates. Collisions between different components are accounted for through the inclusion of a Boltzmann-type collision integral in the hydrodynamic equation. Contrary to standard generalized hydrodynamics, our extended model captures thermalization of the condensate at a rate consistent with experimental observations from a quantum Newton’s cradle setup.

The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.

Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators—magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these nonreciprocal elements have limited performance and are not easily integrated on chip, it has been a long-standing goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.

A cold atomic ensemble suits well for optical quantum memories, and its entanglement with a single photon forms the building block for quantum networks that give promise for many revolutionary applications. Efficiency and lifetime are among the most important figures of merit for a memory. In this Letter, we report the realization of entanglement between an atomic ensemble and a single photon with subsecond lifetime and high efficiency. We engineer dual control modes in a ring cavity to create entanglement and make use of three-dimensional optical lattice to prolong memory lifetime. The memory efficiency is 38% for 0.1 s storage. We verify the atom-photon entanglement after 1 s storage by testing the Bell inequality with a result of $S=2.36\pm 0.14$.

In recent experiments, the light-matter interaction has reached the ultrastrong coupling limit, which can give rise to dynamical generalizations of spatial symmetries in periodically driven systems. Here, we present a unified framework of dynamical-symmetry-protected selection rules based on Floquet response theory. Within this framework, we study rotational, parity, particle-hole, chiral, and time-reversal symmetries and the resulting selection rules in spectroscopy, including symmetry-protected dark states (spDS), symmetry-protected dark bands, and symmetry-induced transparency. Specifically, dynamical rotational and parity symmetries establish spDS and symmetry-protected dark band conditions. A particle-hole symmetry introduces spDSs for symmetry-related Floquet states and also a symmetry-induced transparency at quasienergy crossings. Chiral symmetry and time-reversal symmetry alone do not imply spDS conditions but can be combined to define a particle-hole symmetry. These symmetry conditions arise from destructive interference due to the synchronization of symmetric quantum systems with the periodic driving. Our predictions reveal new physical phenomena when a quantum system reaches the strong light-matter coupling regime, which is important for superconducting qubits, atoms and molecules in optical or plasmonic field cavities, and optomechanical systems.

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson’s rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and $k$-separability are contained in this approach as the diagram’s width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients.

The energy dissipation rate in a nonequilibrium reaction system can be determined by the reaction rates in the underlying reaction network. By developing a coarse-graining process in state space and a corresponding renormalization procedure for reaction rates, we find that energy dissipation rate has an inverse power-law dependence on the number of microscopic states in a coarse-grained state. The dissipation scaling law requires self-similarity of the underlying network, and the scaling exponent depends on the network structure and the probability flux correlation. Existence of the inverse dissipation scaling law is shown in realistic biochemical systems such as biochemical oscillators and microtubule-kinesin active flow systems.

The transition between ergodic and many-body localization (MBL) phases lies at the heart of understanding quantum thermalization of many-body systems. Here, we predict a many-body critical (MBC) phase with finite-size scaling analysis in the one-dimensional extended Aubry-André-Harper-Hubbard model, which is different from both the ergodic phase and MBL phase, implying that the quantum system hosts three different fundamental phases in the thermodynamic limit. The level statistics in the MBC phase are well characterized by the so-called critical statistics, and the wave functions exhibit deep multifractal behavior only in the critical region. We further study the half-chain entanglement entropy and thermalization properties and show that the former, in the MBC phase, manifest a volume law scaling, while the many-body states violate the eigenstate thermalization hypothesis. The results are confirmed by the state-of-the-art numerical calculations with system size up to $L=22$. This work unveils a novel many-body phase which is extended but nonthermal.