The discrimination of two nonorthogonal states is a fundamental element for secure and efficient communication. Quantum measurements of nonorthogonal coherent states can enhance information transfer beyond the limits of conventional technologies. We demonstrate a strategy for binary state discrimination based on optimized single-shot measurements with photon number resolving (PNR) detection with finite number resolution. This strategy enables a high degree of robustness to noise and imperfections while being scalable to high rates and in principle allows for surpassing the quantum noise limit (QNL) in practical situations. These features make the strategy inherently compatible with high-bandwidth communication and quantum information applications, providing advantages over the QNL under realistic conditions.

We present exact solutions of an energy spectrum of 2-interacting particles in which they seem to be relativistic fermions in 2+1 space-time dimensions. The 2x2 spinor equations of 2-interacting fermions through general central potential were separated covariantly into the relative and center of mass coordinates. First of all, the coupled first order differential equations depending on radial coordinate were derived from 2x2 spinor equations. Then, a second order radial differential equation was obtained and solved for Coulomb interaction potential. We apply our solutions to exciton phenomena for a free-standing monolayer medium. Since we regard exciton as isolated 2-interacting fermions in our model, any other external effect such as substrate was eliminated. Our results show that the obtained binding energies in our model are in agreement with the literature. Moreover, the decay time of an exciton was found out spontaneously in our calculations.

The textbook effective-range expansion of scattering theory is useful in the analysis of low-energy scattering phenomenology when the scattering length $|a|$ is much larger than the range $R$ of the scattering potential: $|a|\gg R$. Nevertheless, the same has been used for systems where the scattering length is much smaller than the range of the potential, which could be the case in many scattering problems. We suggest and numerically study improved two-parameter effective-range expansions for the cases $|a| > R$ and $|a| < R$. The improved effective-range expansion for $|a| > R$ reduces to the textbook expansion for $|a|/R \gg 1$.

In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic programming algorithms. In this problem we are asked whether there is a path from $0^n$ to $1^n$ in a given subgraph of the Boolean hypercube, where the edges are all directed from smaller to larger Hamming weight. We give a quantum algorithm that solves path in the hypercube in time $O^*(1.817^n)$. The technique combines Grover's search with computing a partial dynamic programming table. We use this approach to solve a variety of vertex ordering problems on graphs in the same time $O^*(1.817^n)$, and graph bandwidth in time $O^*(2.946^n)$. Then we use similar ideas to solve the travelling salesman problem and minimum set cover in time $O^*(1.728^n)$.

We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the one-shot $\epsilon$-error capacity are formalized as semidefinite programs (SDPs). Based on this, we obtain improved SDP finite blocklength converse bounds of general quantum channels for entanglement-assisted codes and unassisted codes. Furthermore, we derive two SDP strong converse bounds for the classical capacity of general quantum channels: for any code with a rate exceeding either of the two bounds of the channel, the success probability vanishes exponentially fast as the number of channel uses increases. In particular, applying our efficiently computable bounds, we derive an improved upper bound on the classical capacity of the amplitude damping channel. We also establish the strong converse property for the classical and private capacities of a new class of quantum channels. We finally study the zero-error setting and provide efficiently computable upper bounds on the one-shot zero-error capacity of a general quantum channel.

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods like channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences required to obtain rigorous confidence intervals. Previous bounds were either prohibitively loose or required the number of sampled sequences to scale exponentially with the number of qubits in order to obtain a fixed confidence interval at a fixed error rate. Here we show that, with a small adaptation to the randomized benchmarking procedure, the number of sampled sequences required for a fixed confidence interval is dramatically smaller than could previously be justified. In particular, we show that the number of sampled sequences required is essentially independent of the number of qubits and scales favorably with the average error rate of the system under investigation. We also show that the number of samples required for long sequence lengths can be made substantially smaller than previous rigorous results (even for single qubits) as long as the noise process under investigation is not unitary. Our results bring rigorous randomized benchmarking on systems with many qubits into the realm of experimental feasibility.

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.

Photonic lattices - arrays of optical waveguides - are powerful platforms for simulating a range of phenomena, including topological phases. While probing dynamics is possible in these systems, by reinterpreting the propagation direction as "time," accessing long timescales constitutes a severe experimental challenge. Here, we overcome this limitation by placing the photonic lattice in a cavity, which allows the optical state to evolve through the lattice multiple times. The accompanying detection method, which exploits a multi-pixel single-photon detector array, offers quasi-real time-resolved measurements after each round trip. We apply the state-recycling scheme to intriguing photonic lattices emulating Dirac fermions and Floquet topological phases. In this new platform, we also realise a synthetic pulsed electric field, which can be used to drive transport within photonic lattices. This work opens a new route towards the detection of long timescale effects in engineered photonic lattices and the realization of hybrid analogue-digital simulators.

Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell inequalities without quantum violation. They are closely related to another important notion, completely entangled subspaces (CESs), which are those that do not contain any fully separable pure state. Among CESs one finds a class of subspaces in which all vectors are not only entangled, but are genuinely entangled. Here we explore the connection between UPBs and such genuinely entangled subspaces (GESs) and provide classes of nonorthogonal UPBs that lead to GESs for any number of parties and local dimensions. We then show how these subspaces can be immediately utilized for a simple general construction of genuinely entangled states in any such multipartite scenario.

We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators, $\langle O_1 \rangle$ and $\langle O_2 \rangle$, but may not have access to $\langle O_1 O_2 \rangle$. This problem is relevant for the study of localized quantum information in gravity since the set of approximately-local operators in a region may not be closed under arbitrary products. While we cannot naturally associate a density matrix with a state in this setting, it is still possible to define a modular operator for a state, and distinguish between two states using a relative modular operator. These operators are defined on a little Hilbert space, which parameterizes small deformations of the system away from its original state, and they do not depend on the structure of the full Hilbert space of the theory. We extract a class of relative-entropy-like quantities from the spectrum of these operators that measure the distance between states, are monotonic under contractions of the set of available observables, and vanish only when the states are equal. Consequently, these distance-measures can be used to define measures of bipartite and multipartite entanglement. We describe applications of our measures to coarse-grained and fine-grained subregion dualities in AdS/CFT and provide a few sample calculations to illustrate our formalism.

Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational "inverse method," the Eigenstate-to-Hamiltonian Construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function $|\psi_T\rangle$ and produces as output Hamiltonians for which $|\psi_T\rangle$ is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and in this work we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model.

We study photon, phonon statistics and the cross-correlation between photons and phonons in a quadratically coupled optomechanical system. Photon blockade, phonon blockade and strongly anticorrelated photons and phonons can be observed in the same parameter regime with the effective nonlinear coupling between the optical and mechanical modes, enhanced by a strong optical driving field. Interestingly, an optimal value of the effective nonlinear coupling strength for the photon blockade is not within the strong nonlinear coupling regime. This abnormal phenomenon results from the destructive interference between different paths for two-photon excitation in the optical mode with a moderate effective nonlinear coupling strength. Further more, we show that phonon (photon) pairs and correlated photons and phonons can be generated in the strong nonlinear coupling regime with a proper detuning between the weak mechanical driving field and mechanical mode. Our results open up a way to generate anticorrelated and correlated photons and phonons, which may have important applications in quantum information processing.

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting non-locality, such as device-independent randomness generation and quantum key distribution. This relation between non-locality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of non-locality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where n noisy PR-boxes are implemented using n non-communicating pairs of devices, it is known that each PR-box behaves as an independent biased coin: the min-entropy per PR-box is constant with the number of copies. We show that this doesn't hold in more general scenarios where several noisy PR-boxes are implemented from a single pair of devices, either used sequentially n times or producing n outcome bits in a single run. In this case, the min-entropy per PR-box is smaller than the min-entropy of a single PR-box, and it decreases as the number of copies increases.

Entanglement is one of the most intriguing features of quantum theory and a main resource in quantum information science. Ground states of quantum many-body systems with local interactions typically obey an "area law" meaning the entanglement entropy proportional to the boundary length. It is exceptional when the system is gapless, and the area law had been believed to be violated by at most a logarithm for over two decades. Recent discovery of Motzkin and Fredkin spin chain models is striking, since these models provide significant violation of the entanglement beyond the belief, growing as a square root of the volume in spite of local interactions. Although importance of intensive study of the models is undoubted to reveal novel features of quantum entanglement, it is still far from their complete understanding. In this article, we first analytically compute the Renyi entropy of the Motzkin and Fredkin models by careful treatment of asymptotic analysis. The Renyi entropy is an important quantity, since the whole spectrum of an entangled subsystem is reconstructed once the Renyi entropy is known as a function of its parameter. We find non-analytic behavior of the Renyi entropy with respect to the parameter, which is a novel phase transition never seen in any other spin model studied so far. The Renyi entropy grows proportionally to the volume in one phase, whereas it scales as a logarithm of the volume in another phase. The transition point itself forms the third phase of the square-root scaling.

Silicon-vacancy (SiV) center in diamond is a photoluminescence (PL) center with a characteristic zero-phonon line energy at 1.681~eV that acts as a solid-state single photon source and, potentially, as a quantum bit. The majority of the luminescence intensity appears in the zero-phonon line; nevertheless, about 30\% of the intensity manifests in the phonon sideband. Since phonons play an essential role in the operation of this system, it is of importance to understand the vibrational properties of the SiV center in detail. To this end, we carry out density functional theory calculations of dilute SiV centers by embedding the defect in supercells of a size of a few thousand atoms. We find that there exist two well-pronounced quasi-local vibrational modes (resonances) with $A_{2u}$ and $E_u$ symmetries, corresponding to the vibration of the Si atom along and perpendicular to the defect symmetry axis, respectively. Isotopic shifts of these modes explain the isotopic shifts of prominent vibronic features in the experimental SiV PL spectrum. Moreover, calculations show that the vibrational frequency of the $A_{2u}$ mode increases by about 30\% in the excited state with respect to the ground state, while the frequency of the $E_u$ mode increases by about 5\%. These changes explain experimentally observed isotopic shifts of the zero-phonon line energy. We also emphasize possible dangers of extracting isotopic shifts of vibrational resonances from finite-size supercell calculations, and instead propose a method to do this correctly.

Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unification of relativistic quantum mechanics in the Foldy-Wouthuysen representation is discussed.

Author(s): Bijita Sarma and Amarendra K. Sarma

We analyze the photon correlations in an optomechanical system containing two nonlinear optical modes and one mechanical mode which are coupled via a three-mode mixing. Under a weak driving condition, we determine the optimal conditions for photon antibunching in the weak-Kerr-nonlinear regime and f...

[Phys. Rev. A 98, 013826] Published Mon Jul 16, 2018

Author(s): Alexander N. Poddubny and Daria A. Smirnova

We study solitons of the two-dimensional nonlinear Dirac equation with asymmetric cubic nonlinearity. We show that with the nonlinearity parameters specifically tuned, a high degree of localization of both spinor components is enabled on a ring of certain radius. Such ring Dirac soliton can be viewe...

[Phys. Rev. A 98, 013827] Published Mon Jul 16, 2018

Author(s): Erin M. Knutson, Jon D. Swaim, Sara Wyllie, and Ryan T. Glasser

We demonstrate an unseeded multimode four-wave-mixing process in hot Rb85 vapor using two pump beams of the same frequency that cross at a small angle. This results in the simultaneous fulfillment of multiple phase-matching conditions that reinforce one another to produce four intensity-stabilized b...

[Phys. Rev. A 98, 013828] Published Mon Jul 16, 2018

Author(s): Jun Wen, Jian-Qi Zhang, Lei-Lei Yan, Liang Chen, Xiao-Ming Cai, and Mang Feng

Trapped ions offer an excellent platform to investigate fascinating phenomena in quantum physics. Here we propose an experimental scheme to achieve Anderson localization of phonons using an ion chain under irradiation of a laser Bessel beam. The quasiperiodicity comes from the characteristic of the ...

[Phys. Rev. A 98, 013829] Published Mon Jul 16, 2018