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The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual experiment. We propose to avoid this question by replacing the Born rule with two non-probabilistic postulates: (i) the projector associated to the observed outcome must have a positive overlap with the state of the measured system; (ii) statements about observed outcomes are robust, that is, remain valid under small perturbations of the state. We show that the two postulates suffice to retrieve the interpretations of the Born rule that are commonly used for analysing experimental data.

Since unconditionally secure quantum two-party computations are known to be impossible, most existing quantum private comparison (QPC) protocols adopted a third party. Recently, we proposed a QPC protocol which involves two parties only, and showed that although it is not unconditionally secure, it only leaks an extremely small amount of information to the other party. Here we further propose the device-independent version of the protocol, so that it can be more convenient and dependable in practical applications.

A semi-quantum key distribution (SQKD) protocol allows a quantum user and a limited "classical" user to establish a shared secret key secure against an all-powerful adversary. In this work, we present a new SQKD protocol where the quantum user is also limited in her measurement capabilities. We describe the protocol, prove its security, and show its noise tolerance is as high as "fully quantum" QKD protocols.

In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both exactly through numerical calculations as well as analytically using eigenvectors and eigenvalues of the quantum system.

The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced Quantization, relates classical models with their quantum partners differently and leads to satisfactory results for all systems. This paper features enhanced quantization procedures and provides highlights of two examples, a rotationally symmetric model and an ultralocal scalar model, for which canonical quantization fails while enhanced quantization succeeds.

The static second hyperpolarizability is derived from the space-fractional Schr\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter $\alpha$ decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for $\alpha \neq 1$, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of $\alpha \rightarrow 1/2$.

We propose a scheme for preparation of large-scale entangled $GHZ$ states and $W$ states with neutral Rydberg atoms. The scheme mainly depends on Rydberg antiblockade effect, i.e., as the Rydberg-Rydberg-interaction (RRI) strength and the detuning between the atom transition frequency and the classical laser frequency satisfies some certain conditions, the effective Rabi oscillation between the two ground states and the two excitation Rydberg states would be generated. The prominent advantage is that both two-multiparticle $GHZ$ states and two-multiparticle $W$ states can be fused in this model, especially the success probability for fusion of $GHZ$ states can reach unit. In addition, the imperfections induced by the spontaneous emission is also discussed through numerical simulation.

The technique of shortcuts to adiabaticity (STA) has attracted broad attention due to their possible applications in quantum information processing and quantum control. However, most studies published so far have been only focused on Hermitian systems under the rotating-wave approximation (RWA). In this paper, we propose a modified STA technique to realize population transfer for a non-Hermitian system without RWA. We work out an exact expression for the control function and present examples consisting of two- and three-level systems with decay to show the theory. The results suggest that the STA technique presented here is robust for fast passages. We also find that the decay has small effect on the population transfer in the three-level system. To shed more light on the physics behind this result, we reduce the quantum three-level system to an effective two-level one with large detunings. The STA technique of effective two-level system is studied. Thereby the high-fidelity population transfer can be implemented in non-Hermitian systems by our method, and it works even without RWA.

It is well known that Grover's algorithm asymptotically transforms an equal superposition state into an eigenstate (of a given basis). Here, we demonstrate a verification algorithm based on weak measurement which can achieve the same purpose even if the qubit is \textit{not} in an equal superposition state. The proposed algorithm highlights the \textit{distinguishability} between any arbitrary single qubit superposition state and an eigenstate. We apply this algorithm to propose the scheme of a Quantum Locker, a protocol in which any legitimate party can verify his/her authenticity by using a newly developed Quantum One-Time Password (OTP) and retrieve the necessary message from the locker. We formally explicate the working of Quantum Locker in association with the Quantum OTP, which theoretically offers a much higher security against any adversary, as compared to any classical security device.

Speech on the occasion of accepting the Dagmar and Vaclav Havel Foundation VIZE 97 Prize for 2017. Delivered at Prague Crossroads, October 5, 2017

We consider multi-time correlators for output signals from linear detectors, continuously measuring several qubit observables at the same time. Using the quantum Bayesian formalism, we show that for unital (symmetric) evolution in the absence of phase backaction, an $N$-time correlator can be expressed as a product of two-time correlators when $N$ is even. For odd $N$, there is a similar factorization, which also includes a single-time average. Theoretical predictions agree well with experimental results for two detectors, which simultaneously measure non-commuting qubit observables.

By studying the quench dynamics in one-dimensional superlattice systems with inversion symmetry, we find robust crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The physics behind this phenomenon is the emergence of a dynamical Chern number accompanied by unitarily created momentum-time Skyrmions. We also discuss a possible experimental situation based on Bloch-state tomography in ultracold atomic systems. Our work identifies the unique role of topology in quantum dynamics far from equilibrium.

Experiments handling Rydberg atoms near surfaces must necessarily deal with the high sensitivity of Rydberg atoms to (stray) electric fields that typically emanate from adsorbates on the surface. We demonstrate a method to modify and reduce the stray electric field by changing the adsorbates distribution. We use one of the Rydberg excitation lasers to locally affect the adsorbed dipole distribution. By adjusting the averaged exposure time we change the strength (with the minimal value less than $0.2\,\textrm{V/cm}$ at $78\,\mu\textrm{m}$ from the chip) and even the sign of the perpendicular field component. This technique is a useful tool for experiments handling Ryberg atoms near surfaces, including atom chips.

Quantum processors promise a paradigm shift in high-performance computing which needs to be assessed by accurate benchmarking measures. In this work, we introduce a new benchmark for variational quantum algorithm (VQA), recently proposed as a heuristic algorithm for small-scale quantum processors. In VQA, a classical optimization algorithm guides the quantum dynamics of the processor to yield the best solution for a given problem. A complete assessment of scalability and competitiveness of VQA should take into account both the quality and the time of dynamics optimization. The method of optimal stopping, employed here, provides such an assessment by explicitly including time as a cost factor. Here we showcase this measure for benchmarking VQA as a solver for some quadratic unconstrained binary optimization. Moreover we show that a better choice for the cost function of the classical routine can significantly improve the performance of the VQA algorithm and even improving it's scaling properties.

We study the behaviour of two different measures of the complexity of multipartite correlation patterns, weaving and neural complexity, for symmetric quantum states. Weaving is the weighted sum of genuine multipartite correlations of any order, where the weights are proportional to the correlation order. The neural complexity, originally introduced to characterize correlation patterns in classical neural networks, is here extended to the quantum scenario. We derive close formulas of the two quantities for GHZ states mixed with white noise

We consider crystal chirp effects on SPDC when pumping at 800 nm. The typical distribution produced in frequency-momentum space is a pop tab-like structure which turns out to be suitable for the implementation of versatile light sources. Our analyzes consider the effect of internal and external parameters in the process; in the former we include the crystal chirp and length, while in the latter temperature, as well as pump chirp and beam properties. We report evidence of the appropriateness of SPDC from chirped crystals to manipulate the frequency and transverse momentum properties of the light produced. We briefly comment on potential usefulness of the types of light produced, in particular for quantum information applications.