In this paper we propose a protocol for a data compression task, blind quantum data compression, with finite local approximations. The rate of blind data compression is susceptible to approximations even when the approximations are diminutive. This instability originates from the sensitivity of a structure of quantum states against approximations, which makes the analysis of blind compression in the presence of approximations intractable. In this paper we construct a protocol that takes advantage of the instability to reduce the compression rate substantially. Our protocol shows a significant reduction in rate for specific examples we examine. Moreover, we apply our methods to diagonal states and propose two types of approximation methods in this special case. We perform numerical experiments and observe that one of these two approximation methods performs significantly better than the other. Thus, our analysis makes a step toward general investigation of blind quantum data compression with the allowance of approximations towards further investigation of approximation-rate trade-off of blind quantum data compression.

Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution is finite-difference schemes, which can be reduced to the linear algebra problem. We consider three approaches to solve the heat equation on a quantum computer. Using the direct variational method we minimize the expectation value of a Hamiltonian with its ground state being the solution of the problem under study. Typically, an exponential number of Pauli products in the Hamiltonian decomposition does not allow for the quantum speedup to be achieved. The Hadamard-test-based approach solves this problem, however, the performed simulations do not evidently prove that the Ansatz circuit has a polynomial depth with respect to the number of qubits. The Ansatz tree approach exploits an explicit form of the matrix that makes it possible to achieve an advantage over classical algorithms. In our numerical simulations with up to $n=11$ qubits, this method reveals the exponential speedup.

Recent advances in quantum technologies raise the urgent need of verifying the correct functionality of a quantum device. Certifying the correctness of a quantum device in a fully classical manner is an important research branch. In this paper, we present a measurement protocol that allows a classical verifier to interact with an efficient quantum prover to verify the computational basis or the $XY$-plane basis measurement on a quantum state. With the help of two adaptive hardcore bit properties of a noisy trapdoor claw-free family, the security of measurement protocol is proved, which is under quantum hardness of the learning with error. The security characterizes the distance between the output distribution of measurement protocol and the distribution obtained by measuring certain quantum states in the designated basis, with or without the presence of honest behavior of the prover. Moreover, exploiting the measurement protocol, we present two device-noise-independent verification protocols of graph states and a classical verification protocol of delegated quantum computing whose soundness is 0.5757.

Geometric effects can play a pivotal role in streamlining quantum manipulation. We demonstrate a geometric diabatic control, that is, perfect tunneling between spin states in a diamond by a quadratic sweep of a driving field. The field sweep speed for the perfect tunneling is determined by the geometric amplitude factor and can be tuned arbitrarily. Our results are obtained by testing a quadratic version of Berry's twisted Landau-Zener model. This geometric tuning is robust over a wide parameter range. Our work provides a basis for quantum control in various systems, including condensed-matter physics, quantum computation, and nuclear magnetic resonance.

Quantum vortices are often endowed with an effective inertial mass, due, for example, to massive particles in their cores. Such “massive vortices” display new phenomena beyond the standard picture of superfluid vortex dynamics, where mass is neglected. In this work, we demonstrate that massive vortices are allowed to collide, as opposed to their massless counterparts. We propose a scheme to generate controllable, repeatable, deterministic collisional events in pairs of quantum vortices. We demonstrate two mass-driven fundamental processes: (i) the annihilation of two counter-rotating vortices and (ii) the merging of two corotating vortices, thus pointing out new mechanisms supporting incompressible-to-compressible kinetic-energy conversion, as well as doubly quantized vortex stabilization in flat superfluids.

We introduce a formalism to efficiently calculate lasing modes and optical power flow in multisection lasers with open boundaries. The formalism is underpinned by a projection of the complex-valued electric field and its spatial derivative onto a suitably extended complex $\mathcal{Z}$ plane to reduce the order of the problem and simplify analysis. In a single-section laser, we show that a laser mode is a loxodrome on the extended complex $\mathcal{Z}$ plane. In a multisection laser, we obtain loxodromes for individual sections of the laser. Then, a multisection mode is constructed by continuously concatenating individual loxodromes from each section using the open boundary conditions. A natural visualization of this construction is given by stereographic projection of the extended complex $\mathcal{Z}$ plane onto the Riemann sphere. Our formalism simplifies the analysis of lasing modes in open multisection lasers and provides insight into the mode geometry and degeneracy.

We propose a protocol to realize discrimination of chiral molecules based on steady states of a cavity mode. Using the closed-loop three-level structure of a molecule, an effective Hamiltonian of the molecule-cavity-coupled system is derived. The effective Hamiltonian is similar to a linear driving of the cavity mode, but the driving strength depends on the chirality of the molecule. In the presence of photon loss, the cavity behaves like a driven damped harmonic oscillator, and it will evolve to different steady coherence states according to the chirality of the molecule. By selecting proper parameters, it is possible to obtain steady coherence states with large-enough amplitudes that can be well determined by homodyne measurements on the cavity. Consequently, the chirality of the molecules can be discriminated near perfectly, according to the measurement result of the cavity. Numerical simulations show that the protocol is insensitive to the systematic errors of the control fields and the energy relaxation of the molecules. Therefore, the protocol may provide an effective approach to realize chirality discrimination with high accuracy.

Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place, which is pertinent for design and control of quantum technologies. In this paper, we derive speed limits on correlations such as entanglement, Bell-CHSH correlation, and quantum mutual information of quantum systems evolving under dynamical processes. Our main result is a speed limit on an entanglement monotone called negativity, which holds for arbitrary-dimensional bipartite quantum systems and processes. Another entanglement monotone which we consider is the concurrence. To illustrate the efficacy of our speed limits, we analytically and numerically compute the speed limits on the negativity, concurrence, and Bell-CHSH correlation for various quantum processes of practical interest. We are able to show that, for practical examples we have considered, some of the speed limits we derived are actually attainable and hence these bounds can be considered to be tight.

We show that the quantum teleportation protocol is a powerful tool to study quantum phase transitions at finite temperatures. We consider a pair of spins from an infinite spin-1/2 chain ($XXZ$ model) in equilibrium with a reservoir at temperature $T$ as the resource used by Alice and Bob to implement the teleportation protocol. We show that the efficiency of this pair of spins to teleport a qubit is drastically affected after we cross a quantum critical point (QCP), even for high values of $T$. Also, we show that the present tool is as sharp as quantum discord (QD) to spotlight a QCP, where QD is the best finite $T$ QCP detector known to date. Contrary to QD, however, we show that the present tool is easier to compute theoretically and has a direct experimental and operational meaning.

The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale $\hslash$, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work we introduce compasslike states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that when a significant quantity of photons is added (or subtracted), the Wigner functions of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon-addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon-subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.

Here we introduce interferometric devices by combining optical feedback (cavities) with unbiased multiports, which, unlike traditional beam dividers, allow light to reflect back out of the port from which it originated. By replacing the traditional, directionally biased beam-splitter in a Michelson interferometer with an unbiased multiport, the functional dependence of the scattering amplitudes changes. As a result, the derivative of transmittance with respect to an external phase perturbation can be made substantially large. This significantly enhances the resolution of phase measurement and allows the phase response curves to be altered in real time by tuning an externally controllable phase shift.

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper we investigate the influence of symmetry-breaking perturbations upon ground-state nonlocality by considering several typical finite-size quantum models, including the transverse-field Ising chains, the $XY$($XX$) chains, and the $XXZ$ chains. We find that even a slight perturbation can reshape the nonlocality curve dramatically. For instance, in the $XY$ chains, a perturbation can induce an oscillation behavior in the nonlocality curve. A clear microscopic mechanism for the results is proposed. Furthermore, we also connect the behaviors to the macroscopic symmetry properties of the chains and make some predictions on general models.

We propose an efficient nonlinear readout scheme for entangled non-Gaussian spin states based on the intrinsic quasicyclic dynamics of interacting spin-$\frac{1}{2}$ systems. We focus on two well-known spin models of twist-and-turn (TNT) and two-axis-countertwisting (TACT), where the entangled non-Gaussian spin state can be generated by spin dynamics starting from unstable fixed points. In the TNT model, the non-Gaussian probe state evolves directly back to the vicinity of the initial state during the subsequent time-forward evolution for path recombining, accompanied by quantum magnification of an encoded signal and refocusing of the associated quantum noise. Based on low-order moment measurement, we find that the optimal metrological gain nearly saturates the quantum Cramér-Rao bound (QCRB) and follows the Heisenberg scaling. For the TACT case, the QCRB can also be nearly approached when the state converges to either of the two unstable fixed points corresponding to the initial state or its orthogonal coherent state, respectively. The latter case goes beyond previous studies where tracing back to or crossing the initial states was mostly considered. The present protocol does not require time reversal as in typical nonlinear interferometries and it also avoids complicated measurement of nonlinear observables or full probability distributions. The operational approach we discuss presents a practical way to realize high-precision and detection-noise-robust quantum metrology with entangled non-Gaussian spin states.

In this paper, we investigate the coherent control over a complex multilevel atomic system using the stimulated Raman adiabatic passage. Based on the example of ${}^{87}\mathrm{Rb}$ atoms, excited with circularly polarized light at the $D_1$ line, we demonstrate the ability to decompose the system into three- and four-level subsystems independently interacting with light beams. Focusing on the four-level system, we demonstrate that the presence of an additional excited state significantly affects the dynamics of the system evolution. Specifically, it is shown that, through the appropriate tuning of the light beams, some of the transfer channels can be blocked, which leads to better control over the system. We also demonstrate that this effect is most significant in media free from inhomogeneous broadening (e.g., Doppler effect) and deteriorates if such broadening is present. For instance, the motion of atoms affects both the efficiency and selectivity of the transfer.

We study the response of an optical system with the Kerr nonlinearity demonstrating Bloch oscillations to a periodic train of coherent pulses. It has been found out that the intensity of the field excited in the system by pulses resonantly depends on the train period. It is demonstrated numerically and analytically that the response of the system is stronger when the period of the driving pulses is commensurate with the period of the Bloch oscillations. Moreover, large enough pulses are capable to induce the instabilities which eventually lead to onset of chaotic Bloch oscillations of the wave-function envelope bouncing both in time and space. The analysis reveals that these instabilities are associated with period-doubling bifurcations. A cascade of such bifurcations with increase of the pulse amplitude triggers the chaotic behavior.

The quantum state discrimination primitive becomes highly nontrivial in the limited measurement setting and leads to different classes of impossibility, viz., indistinguishability, unmarkability, irreducibility, etc. These phenomena, often referred to as another nonlocal aspect of quantum theory, have utmost importance in the domain of data hiding, secret sharing, etc. Motivated by this, recently a significant effort has been devoted to activate local indistinguishability from locally distinguishable nontrivial sets of quantum states. In the present work, we introduce other stronger notions of quantum nonlocality and depict a series of hierarchical nonlocality activation from nontrivial sets of locally distinguishable entangled states. Moreover, we appropriately moderate the strict condition of nontriviality, introduced in earlier literature, and come up with interesting examples in support of our claim.

We analyze an all-optical setup which enables Bell-inequality violation over long distances by exploiting probabilistic entanglement swapping. The setup involves only two-mode squeezers, displacements, beamsplitters, and on-off detectors. We describe how events must be arranged to close both the detection and locality loopholes. We analyze a scenario with dichotomic inputs and outputs, and check the robustness of the Bell inequality violation for up to six parties, with respect to phase, amplitude, and dark count noise, as well as loss.