Author(s): Murphy Yuezhen Niu, Isaac L. Chuang, and Jeffrey H. Shapiro

We prove that universal quantum computation can be realized—using only linear optics and χ(2) (three-wave mixing) interactions—in any (n+1)-dimensional qudit basis of the n-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next...

[Phys. Rev. Lett. 120, 160502] Published Wed Apr 18, 2018

Author(s): F. Fratini, L. Safari, P. Amaro, and J. P. Santos

We developed a method to calculate two-photon processes in quantum mechanics that replaces the infinite summation over the intermediate states by a perturbation expansion. This latter consists of a series of commutators that involve position, momentum, and Hamiltonian quantum operators. We analyzed ...

[Phys. Rev. A 97, 043842] Published Wed Apr 18, 2018

Author(s): L. Clark, H. G. Brown, D. M. Paganin, M. J. Morgan, T. Matsumoto, N. Shibata, T. C. Petersen, and S. D. Findlay

The rigid-intensity-shift model of differential-phase-contrast imaging assumes that the phase gradient imposed on the transmitted probe by the sample causes the diffraction pattern intensity to shift rigidly by an amount proportional to that phase gradient. This behavior is seldom realized exactly i...

[Phys. Rev. A 97, 043843] Published Wed Apr 18, 2018

Author(s): Nicolai B. Grosse, Philipp Franz, Jan Heckmann, Karsten Pufahl, and Ulrike Woggon

Optical media endowed with large nonlinear susceptibilities are highly prized for their employment in frequency conversion and the generation of nonclassical states of light. Although the presence of an optical resonance can greatly increase the nonlinear response (e.g., in epsilon-near-zero materia...

[Phys. Rev. A 97, 043844] Published Wed Apr 18, 2018

Author(s): C. E. Máximo, R. Bachelard, and R. Kaiser

Dielectric spheres moving in a dissipative medium are subjected to the effects of optical binding, i.e., a net force resulting from the collective scattering of light. Optical binding is now shown to exist with frictionless cold atoms, bringing as an additional feature the existence of rotating bound states.

[Phys. Rev. A 97, 043845] Published Wed Apr 18, 2018

Author(s): Eiki Iyoda and Takahiro Sagawa

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is de...

[Phys. Rev. A 97, 042330] Published Wed Apr 18, 2018

Author(s): Cong Jiang, Zong-Wen Yu, and Xiang-Bin Wang

We present an analysis for measurement-device-independent quantum key distribution with correlated source-light-intensity errors. Numerical results show that the results here can greatly improve the key rate especially with large intensity fluctuations and channel attenuation compared with prior res...

[Phys. Rev. A 97, 042331] Published Wed Apr 18, 2018

Author(s): Jeong San Kim

We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary-dimensional quantum systems. By using the βth power of entanglement of assistance for 0≤β≤1 and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of...

[Phys. Rev. A 97, 042332] Published Wed Apr 18, 2018

Spatial structure of photons renders them extremely versatile carriers of quantum information, as it can be tailored with simple optical elements such as lenses, phase gratings or holograms. Substantial challenges emerge, however, when such spatially-structured photons carrying quantum information need to be stored in quantum memories or if advanced quantum information processing capability beyond linear optics is required. These quandaries are usually not shared by material systems, for which strong interaction can be engineered, leading to efforts in demonstrating quantum-interferometric properties of atoms, phonons or plasmons. Here we harness the full three-dimensional potential of material quasi-particles - collective atomic excitations known as spin waves. We demonstrate that the spatial structure of single spin waves can be manipulated via the off-resonant ac-Stark shift. Through spin-wave diffraction based beam-splitter transformation, we realize the Hanbury Brown-Twiss (HBT) type measurement at the spin-wave level, demonstrating nonclassical statistics of atomic excitations. Finally, we observe interference of two spin waves - an analogue of the Hong-Ou-Mandel (HOM) effect for photons. Thanks to the reversible photon-spin wave mapping via the Duan-Lukin-Cirac-Zoller (DLCZ) protocol, these techniques enable encoding states from a high-dimensional Hilbert space into the spatial structure of spin waves to facilitate not only new quantum communication schemes, but also high data rate classical telecommunication.

In this work we study the problem of single-shot discrimination of von Neumann measurements. We associate each measurement with a measure-and-prepare channel. There are two possible approaches to this problem. The first one, which is simple, does not utilize entanglement. We focus only on discrimination of classical probability distribution, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage and entanglement. We quantify the distance of the two measurements in terms of the diamond norm (called sometimes the completely bounded trace norm). We provide an exact expression for the optimal probability of correct distinction and relate it to the discrimination of unitary channels. We also state a necessary and sufficient condition for perfect discrimination and a semidefinite program which checks this condition. Our main result, however, is a cone program which calculates the distance of these measurements and hence provides an upper bound on the probability of their correct distinction. As a by-product the program also finds a strategy (input state) which achieves this bound. Finally, we provide a full description for the cases of Fourier matrices and mirror isometries.

We provide an alternative proof of Wallman's \cite{Wallman2018} bounds on the effect of gate-dependent noise on randomized benchmarking (RB). Our primary insight is that a RB sequence is a convolution amenable to Fourier space analysis, and we adopt the mathematical framework of Fourier transforms of matrix-valued functions on groups established in recent work from Gowers and Hatami \cite{GH15}. We show explicitly that as long as our faulty gate-set is close to some representation of the Clifford group, an RB sequence is described by the exponential decay of a process that has exactly two eigenvalues close to one and the rest close to zero, even though the bounds with respect to any particular representation of the Clifford group may not tightly describe the rate of decay. This framework reveals some very provocative properties of maximally entangled states, and likely has applications in other areas of quantum information theory.

To study potential limitations of controllability of physical systems I have earlier proposed physically universal cellular automata and Hamiltonians. These are translation invariant interactions for which any control operation on a finite target region can be implemented by the autonomous time evolution if the complement of the target region is 'programmed' to an appropriate initial state. This provides a model of control where the cut between a system and its controller can be consistently shifted, in analogy to the Heisenberg cut defining the boundary between a quantum system and its measurement device. However, in the known physically universal CAs the implementation of microscopic transformations requires to write the 'program' into microscopic degrees of freedom, while human actions take place on the macroscopic level. I therefore ask whether there exist physically universal interactions for which any desired operation on a target region can be performed by only controlling the macroscopic state of its surrounding. A very simple argument shows that this is impossible with respect to the notion of 'macroscopic' proposed here: control devices whose position is only specified up to 'macroscopic precision' cannot operate at a precise location in space. This suggests that reasonable notions of `universal controllability' need to be tailored to the manipulation of relative coordinates, but it is not obvious how to do this. The statement that any microscopic transformation can be implemented in principle, whenever it is true in any sense, it does not seem to be true in its most obvious sense.

A conceptual design for a quantum blockchain is proposed. Our method involves encoding the blockchain into a temporal GHZ (Greenberger-Horne-Zeilinger) state of photons that do not simultaneously coexist. It is shown that the entanglement in time, as opposed to an entanglement in space, provides the crucial quantum advantage. All the subcomponents of this system have already been shown to be experimentally realized. Perhaps more shockingly, our encoding procedure can be interpreted as non-classically influencing the past; hence this decentralized quantum blockchain can be viewed as a quantum networked time machine.

In the present work we introduce a computational approach to the absolute rovibrational quantum partition function using the path-integral formalism of quantum mechanics in combination with the nested sampling technique. The numerical applicability of path-integral nested sampling is demonstrated for small molecules of spectroscopic interest. The computational cost of the method is determined by the evaluation time of a point on the potential-energy surface (PES). For efficient PES implementations, the path-integral nested-sampling method can be a viable alternative to the direct Boltzmann summation technique of variationally computed rovibrational energies, especially for medium-sized molecules and at elevated temperatures.

We establish an operational measure for quantum coherence with affinity, a notion similar to fidelity. That is, we introduce the square affinity coherence and give the analytic formula for this coherence measure. Moreover, we provide an operational interpretation for this coherence measure, by proving that the corresponding coherence is equal to the error probability to discrimination a set of pure states with least square measurement. Besides, we study its convex roof and show that it is a different coherence measure, not like geometric coherence. Based on the roles they play in quantum state discrimination, we make a comparison between geometric coherence and these quantifiers. Following the same idea, we introduce a family of coherence measures with the generalization of affinity, these are also the special case of $\alpha$-$z$-relative R$\acute{\mathrm{e}}$nyi entropy.

We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It gives a possibility to find exact solution for the energy spectrum of the generalized Dirac oscillator in nonuniform electric field. Explicit examples of exact solutions are presented. We show that sufficiently large electric field destroys the bounded eigenstates.

With experimental quantum computing technologies now in their infancy, the search for efficient means of testing the correctness of these quantum computations is becoming more pressing. An approach to the verification of quantum computation within the framework of interactive proofs has been fruitful for addressing this problem. Specifically, an untrusted agent (prover) alleging to perform quantum computations can have his claims verified by another agent (verifier) who only has access to classical computation and a small quantum device for preparing or measuring single qubits. However, when this quantum device is prone to errors, verification becomes challenging and often existing protocols address this by adding extra assumptions, such as requiring the noise in the device to be uncorrelated with the noise on the prover's devices. In this paper, we present a simple protocol for verifying quantum computations, in the presence of noisy devices, with no extra assumptions. This protocol is based on post hoc techniques for verification, which allow for the prover to know the desired quantum computation and its input. We also perform a simulation of the protocol, for a one-qubit computation, and find the error thresholds when using the qubit repetition code as well as the Steane code.

We unify and consolidate various results about non-signall-ing games, a subclass of non-local two-player one-round games, by introducing and studying several new families of games and establishing general theorems about them, which extend a number of known facts in a variety of special cases. Among these families are {\it reflexive games,} which are characterised as the hardest non-signalling games that can be won using a given set of strategies. We introduce {\it imitation games,} in which the players display linked behaviour, and which contains as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and {\it unique} games. We associate a C*-algebra $C^*(\mathcal{G})$ to any imitation game $\mathcal{G}$, and show that the existence of perfect quantum commuting (resp.\ quantum, local) strategies of $\mathcal{G}$ can be characterised in terms of properties of this C*-algebra, extending known results about synchronous games. We single out a subclass of imitation games, which we call {\it mirror games,} and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra. We describe the main classes of non-signalling correlations in terms of states on operator system tensor products.

Classicalization is a phenomenon of redistribution of energy - initially stored in few hard quanta - into the high occupation numbers of the soft modes, described by a final state that is approximately classical. Using an effective Hamiltonian, we first show why the transition amplitudes that increase occupation numbers are exponentially suppressed and how a very special family of classicalizing theories compensates this suppression. This is thanks to a large micro-state entropy generated by the emergent gapless modes around the final classical state. The dressing of the process by the super-soft quanta of these modes compensates the exponential suppression of the transition probability. Hence, an unsuppressed classicalization takes place exclusively into the states of exponentially enhanced memory storage capacity. Next, we describe this phenomenon in the language of a quantum neural network, in which the neurons are represented as interconnected quantum modes with gravity-like negative-energy synaptic connections. We show that upon an injection of energy in form of a hard quantum stimulus, the network reaches the classicalized state of exponentially enhanced memory capacity with order one probability. We construct a simple model in which the transition results into classical states that carry an area-law micro-state entropy. In this language, a non-Wilsonian UV-completion of the Standard Model via classicalization implies that above cutoff energy the theory operates as a brain network that softens the high energy quanta by bringing itself into the state of a maximal memory capacity. A similar interpretation applies to black hole formation in particle collision.

We experimentally study the effect of a slight nonorthogonality in a two-dimensional optical lattice onto resolved-sideband Raman cooling. We find that when the trap frequencies of the two lattice directions are equal, the trap frequencies of the combined potential exhibit an avoided crossing and the corresponding eigenmodes are rotated by 45 gerees relative to the lattice beams. Hence, tuning the trap frequencies makes it possible to rotate the eigenmodes such that both eigenmodes have a large projection onto any desired direction in the lattice plane, in particular, onto the direction along which Raman cooling works. Using this, we achieve two-dimensional Raman ground-state cooling in a geometry where this would be impossible, if the eigenmodes were not rotated. Our experiment is performed with a single atom inside an optical resonator but this is inessential and the scheme is expected to work equally well in other situations.