# Quantum Physics

## New submissions

[ total of 37 entries: 1-37 ]
[ showing up to 2000 entries per page: fewer | more ]

### New submissions for Mon, 25 Sep 17

[1]
Title: Verification of many-qubit states
Subjects: Quantum Physics (quant-ph)

Verification is a task to check whether a given quantum state is correct or not. If a verifier does not have enough ability to generate the correct state by oneself, verification is a highly non-trivial problem. In this paper, we show that a variety of many-qubit quantum states can be verified with only sequential single-qubit measurements of Pauli operators. First, we introduce a protocol for the verification of ground states of Hamiltonians. We next explain how to verify quantum states generated by a certain class of unitary quantum circuits. We finally consider an adaptive test of stabilizers that enables the verification of any polynomial-time-generated hypergraph state, which include output states of the Bremner-Montanaro-Shepherd type instantaneous quantum polynomial time (IQP) circuits. Importantly, all our protocols do not assume any i.i.d. property of samples: our protocols work even if some highly complicated entanglement is created among samples in any artificial way by a malicious server. As an application, we show that our third protocol can be used for the verification of the quantum supremacy demonstration with the IQP model and its variants.

[2]
Title: Quantum mechanics of orthogonal polynomials
Authors: A. D. Alhaidari
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in the energy. All information about the corresponding physical system (both structural and dynamical) are derived from the properties of these polynomials. An advantage of this formulation is that the class of exactly solvable problems becomes larger than in the conventional formulation (see, for example, Table 1 in the text).

[3]
Title: Symmetry-breaking dynamics of the finite-size Lipkin-Meshkov-Glick model near ground state
Subjects: Quantum Physics (quant-ph)

We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with finite number of spins. In the thermodynamic limit, the ground state of the LMG model with isotropic Hamiltonian in broken phase breaks to a mean-field ground state with a certain direction. However, when the spins number $N$ is finite, the exact ground state is always unique and is not given by a classical mean-field ground state. Here we prove that for $N$ is large but finite, through a tiny external perturbation ($\sim O(1/N^2)$ or less), a localized state which is close to a mean-field ground state can be prepared, which mimics a spontaneous symmetry breaking (SSB). Besides, we find the localized in-plane spin polarization oscillates with two different frequencies $\sim O(1/N)$, and the lifetime of the localized state is exponentially large with respect to $N$. We numerically test the analytical results and find that they fit with each other very well. Finally, we link the phenomena to quantum time crystals and quasicrystals.

[4]
Title: Locality at the boundary implies gap in the bulk for 2D PEPS
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing that if the boundary state of any rectangular subregion is a quasi-local Gibbs state of the virtual indices, then the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit. The proof employs the martingale method of nearly commuting projectors, and exploits a result of Araki on the robustness of one dimensional Gibbs states. Our result provides one of the first rigorous connections between boundary theories and dynamical properties in an interacting many body system. We show that the proof can be extended to MPO-injective PEPS, and speculate that the assumption on the locality of the boundary Hamiltonian follows from exponential decay of correlations in the bulk.

[5]
Title: Role of Hypothesis Testing in Quantum Information
Authors: Masahito Hayashi
Comments: This is the manuscript for Proceeding of AQIS2017
Subjects: Quantum Physics (quant-ph)

Recently, it is well recognized that hypothesis testing has deep relations with other topics in quantum information theory as well as in classical information theory. These relations enable us to derive precise evaluation in the finite-length setting. However, such usefulness of hypothesis testing is not limited to information theoretical topics. For example, it can be used for verification of entangled state and quantum computer as well as guaranteeing the security of keys generated via quantum key distribution. In this talk, we overview these kinds of applications of hypothesis testing.

[6]
Title: Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
Subjects: Quantum Physics (quant-ph)

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cram\'er-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost important in realistic scenarios, such as observational astronomy.

[7]
Title: Past of a particle in an entangled state
Subjects: Quantum Physics (quant-ph)

Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the "weak trace" it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with non-trivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the past of pairs, triplets and eventually the entire system, including higher-order, multipartite traces in the analysis. This resonates with a recently proposed top-down approach by Aharonov, Cohen and Tollaksen for understanding the structure of correlations in pre- and postselected systems.

[8]
Title: Emulating many-body localization with a superconducting quantum processor
Subjects: Quantum Physics (quant-ph)

The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization that only addresses noninteracting particles in the presence of disorder, greatly challenges this concept because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment of fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.

[9]
Title: High-sensitivity measurement of Rydberg population via two-photon excitation in atomic vapour using optical heterodyne detection technique
Comments: 6 pages and 5 figures. arXiv admin note: text overlap with arXiv:1605.06603
Subjects: Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph)

We demonstrate a technique based on optical heterodyne detection to measure Rydberg population in thermal atomic vapour. The technique used a probe beam far off resonant to the D2 line of rubidium along with a reference beam with frequency offset by 800 MHz in the presence of a coupling laser that couples to Rydberg state via two-photon resonance. The polarizations of the probe, reference and coupling beams are suitably chosen such that only the probe beam goes through a non-linear phase shift due to two-photon process which is measured relative to the phase shift of the reference beam using optical heterodyne detection technique. We show that the technique has a sensitivity to measure the minimum phase shift of the order of few $\mu$rad. We have used a suitable model of two-photon excitation of a 3-level atom to show that the minimum phase shift measured in our experiment corresponds to Rydberg population of the order of $10^{-5}$. The corresponding probe absorption for the given laser parameters is of the order of $10^{-7}$. Direct measurement of such a small probe absorption can't be reliable since it will be obscured due to the effect of small polarization impurities in the probe and the coupling beams. We demonstrate that this technique is insensitive to such polarization impurity or fluctuations in the beams and hence, provides a reliable measurement of the Rydberg population. The technique is particularly useful in measuring Rydberg excitation in thermal vapour where multi channel plates (MCP) can't be used due to presence of surface charges. It can also be used in ultra-cold atomic sample with suitable laser parameters.

[10]
Title: Compact localized states and flat bands from local symmetry partitioning
Comments: 10 pages, 6 figures, 1 appendix
Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one- and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.

[11]
Title: Quantum Memristors in Quantum Photonics
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE); Machine Learning (stat.ML)

We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that this tunable beam splitter, when equipped with weak measurements and classical feedback, behaves as a quantum memristor. Indeed, in order to prove its quantumness, we show how to codify quantum information in the coherent beams. Moreover, we estimate the memory capability of the quantum memristor. Finally, we show the feasibility of the proposed setup in integrated quantum photonics.

[12]
Title: Markovian Matrix Product Density Operators : Efficient computation of global entropy
Authors: Isaac H. Kim
Subjects: Quantum Physics (quant-ph)

We introduce the Markovian matrix product density operator, which is a special subclass of the matrix product density operator. We show that the von Neumann entropy of such ansatz can be computed efficiently on a classical computer. This is possible because one can efficiently certify that the global state forms an approximate quantum Markov chain by verifying a set of inequalities. Each of these inequalities can be verified in time that scales polynomially with the bond dimension and the local Hilbert space dimension. The total number of inequalities scale linearly with the system size.
We use this fact to study the complexity of computing the minimum free energy of local Hamiltonians at finite temperature. To this end, we introduce the free energy problem as a generalization of the local Hamiltonian problem, and study its complexity for a class of Hamiltonians that describe quantum spin chains. The corresponding free energy problem at finite temperature is in NP if the Gibbs state of such Hamiltonian forms an approximate quantum Markov chain with an error that decays exponentially with the width of the conditioning subsystem.

[13]
Title: Quenches across the self-organization transition in multimode cavities
Subjects: Quantum Physics (quant-ph)

A cold dilute atomic gas in an optical resonator can be radiatively cooled by coherent scattering processes when the driving laser frequency is tuned close but below the cavity resonance. When sufficiently illuminated, moreover, the atoms' steady state undergoes a phase transition from homogeneous density to crystalline order. We characterize the dynamics of this self-ordering process in the semi-classical regime when distinct cavity modes with commensurate wavelengths are quasi-resonantly driven by laser fields via scattering by the atoms. The lasers are simultaneously applied and uniformly illuminate the atoms, their frequencies are chosen so that the atoms are cooled by the radiative processes, their intensity is either suddenly switched or slowly ramped across the self-ordering transition. Numerical simulations for different ramp protocols predict that the system exhibits long-lived metastable states, whose occurrence strongly depends on initial temperature, ramp speed, and number of atoms.

[14]
Title: Generalized Quantum Reinforcement Learning with Quantum Technologies
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)

We propose a protocol to perform generalized quantum reinforcement learning with quantum technologies. At variance with recent results on quantum reinforcement learning with superconducting circuits [L. Lamata, Sci. Rep. 7, 1609 (2017)], in our current protocol coherent feedback during the learning process is not required, enabling its implementation in a wide variety of quantum systems. We consider diverse possible scenarios for an agent, an environment, and a register that connects them, involving multiqubit and multilevel systems, as well as open-system dynamics. We finally propose possible implementations of this protocol in trapped ions and superconducting circuits. The field of quantum reinforcement learning with quantum technologies will enable enhanced quantum control, as well as more efficient machine learning calculations.

### Cross-lists for Mon, 25 Sep 17

[15]  arXiv:1709.07461 (cross-list from cond-mat.stat-mech) [pdf, other]
Title: Dynamical quantum phase transitions: a review
Authors: Markus Heyl
Subjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research.

[16]  arXiv:1709.07632 (cross-list from physics.atom-ph) [pdf, other]
Title: Quantum Biomimetic Modeling of Diamond NV$^{-}$ Center Spin Dynamics
Subjects: Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)

The spin dynamics of the diamond NV$^{-}$ center turns out to be similar to that of the chemical compass responsible for avian magnetoreception. We present a simulation framework based on quantum master equation for the former that is based upon the Radical Pair model of the latter. We show that this framework captures all the experimentally studied behavior of the NV$^{-}$ center spin system and can therefore be a predictive modeling tool.

[17]  arXiv:1709.07770 (cross-list from cond-mat.mes-hall) [pdf, other]
Title: Retardation effects on the dispersion and propagation of plasmons in metallic nanoparticle chains
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics); Quantum Physics (quant-ph)

We consider a chain of regularly-spaced spherical metallic nanoparticles, where each particle supports three degenerate localized surface plasmons. Due to the dipolar interaction between the nanoparticles, the localized plasmons hybridize to form extended collective modes. Using an open quantum system approach in which the collective plasmons are coupled to vacuum electromagnetic modes and which, importantly, readily incorporates retardation via the light-matter coupling, we analytically evaluate the radiative frequency shifts of the plasmonic bandstructure. For subwavelength-sized nanoparticles, our analytical treatment provides an excellent quantitative agreement with the results stemming from laborious numerical calculations based on fully-retarded solutions to Maxwell's equations. We further study the impact of retardation effects on the propagation of plasmonic excitations along the chain. While for the longitudinal modes, retardation has a negligible effect, we find that the retarded dipolar interaction can significantly modify the plasmon propagation in the case of transverse-polarized modes. Moreover, our results elucidate the analogy between radiative effects in nanoplasmonic systems and the cooperative Lamb shift in atomic physics.

[18]  arXiv:1709.07792 (cross-list from cond-mat.quant-gas) [pdf, other]
Title: Kapitza stabilization of a repulsive Bose-Einstein condensate in an oscillating optical lattice
Subjects: Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

We show that the Kapitza stabilization can occur in the context of nonlinear quantum fields. Through this phenomenon, an amplitude-modulated lattice can stabilize a Bose-Einstein condensate with repulsive interactions and prevent the spreading for long times. We present a classical and quantum analysis in the framework of Gross-Pitaevskii equation, specifying the parameter region where stabilization occurs. Effects of nonlinearity lead to a significant increase of stability domain comparing to the classical case. Our proposal can be experimentally implemented with current cold atom settings.

[19]  arXiv:1709.07851 (cross-list from math.CO) [pdf, other]
Title: Universal points in the asymptotic spectrum of tensors
Subjects: Combinatorics (math.CO); Computational Complexity (cs.CC); Quantum Physics (quant-ph)

The asymptotic restriction problem for tensors is to decide, given tensors $s$ and $t$, whether the $n$th tensor power of $s$ can be obtained from the $(n+o(n))$th tensor power of $t$ by applying linear maps to the tensor legs (this we call restriction), when $n$ goes to infinity. In this context, Volker Strassen, striving to understand the complexity of matrix multiplication, introduced in 1986 the asymptotic spectrum of tensors. Essentially, the asymptotic restriction problem for a family of tensors $X$, closed under direct sum and tensor product, reduces to finding all maps from $X$ to the reals that are monotone under restriction, normalised on diagonal tensors, additive under direct sum and multiplicative under tensor product, which Strassen named spectral points. Strassen created the support functionals, which are spectral points for oblique tensors, a strict subfamily of all tensors.
Universal spectral points are spectral points for the family of all tensors. The construction of nontrivial universal spectral points has been an open problem for more than thirty years. We construct for the first time a family of nontrivial universal spectral points over the complex numbers, using quantum entropy and covariants: the quantum functionals. In the process we connect the asymptotic spectrum to the quantum marginal problem and to the entanglement polytope.
To demonstrate the asymptotic spectrum, we reprove (in hindsight) recent results on the cap set problem by reducing this problem to computing asymptotic spectrum of the reduced polynomial multiplication tensor, a prime example of Strassen. A better understanding of our universal spectral points construction may lead to further progress on related questions. We additionally show that the quantum functionals are an upper bound on the recently introduced (multi-)slice rank.

### Replacements for Mon, 25 Sep 17

[20]  arXiv:1609.04249 (replaced) [pdf, ps, other]
Title: Virtual photons in the ground state of a dissipative system
Comments: Nature Communications, accepted for publication
Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
[21]  arXiv:1702.07721 (replaced) [pdf, other]
Title: Obtaining highly excited eigenstates of the localized XX chain via DMRG-X
Subjects: Statistical Mechanics (cond-mat.stat-mech); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)
[22]  arXiv:1704.01035 (replaced) [pdf, other]
Title: Optimal discrimination of single-qubit mixed states
Journal-ref: Phys. Rev. A 96, 022312 (2017)
Subjects: Quantum Physics (quant-ph)
[23]  arXiv:1704.01589 (replaced) [pdf, other]
Title: Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks
Journal-ref: Phys. Rev. X 7, 031048 (2017)
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
[24]  arXiv:1704.01710 (replaced) [pdf, other]
Title: The one step fermionic ladder
Comments: 13 pages,9 figures, 4 tables. arXiv admin note: text overlap with arXiv:1608.05826
Journal-ref: Physica E, vol.94, pp 216-30 (2017)
Subjects: Strongly Correlated Electrons (cond-mat.str-el); Quantum Physics (quant-ph)
[25]  arXiv:1705.00031 (replaced) [pdf, ps, other]
Title: Phase-covariant cloning via adiabatic passage in fiber-nanocavity system
Comments: 6 pages, 9 figures,two columns
Subjects: Quantum Physics (quant-ph)
[26]  arXiv:1705.03017 (replaced) [pdf, other]
Title: Optimal continuous variable quantum teleportation with limited resources
Comments: 6 pages, 1 figure; close to published version
Journal-ref: Phys. Rev. Lett. 119, 120503 (2017)
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
[27]  arXiv:1705.04335 (replaced) [pdf, ps, other]
Title: Quantum and private capacities of low-noise channels
Comments: 24 pages, 4 figures, comments welcome! v2: improved bounds on degradability parameters and capacities of depolarizing channel and XZ channel (see also ancillary files 'depol-deg-bound.nb' and 'XZ-deg-bound.nb'), extension of results to generalized low-noise channels
Subjects: Quantum Physics (quant-ph)
[28]  arXiv:1705.10892 (replaced) [pdf, other]
Title: Thermal production, protection and heat exchange of quantum coherences
Comments: 9 pages, 4 figures. Close to published version
Journal-ref: Phys. Rev. A 96, 032117 (2017)
Subjects: Quantum Physics (quant-ph)
[29]  arXiv:1706.02601 (replaced) [pdf, other]
Title: Eigenstate thermalization hypothesis in quantum dimer models
Comments: replaced with published version, 9 pages, 11 figures, 2 tables
Journal-ref: Phys. Rev. B 96, 115140 (2017)
Subjects: Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
[30]  arXiv:1706.06312 (replaced) [pdf, other]
Title: Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture
Journal-ref: Physical Review Letters 119, 120504 (2017)
Subjects: Quantum Physics (quant-ph)
[31]  arXiv:1706.08676 (replaced) [pdf, other]
Title: Measurement of complete and continuous Wigner functions for discrete atomic systems
Subjects: Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph); Optics (physics.optics)
[32]  arXiv:1707.01820 (replaced) [pdf, other]
Title: Typical equilibrium state of an embedded quantum system
Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
[33]  arXiv:1707.06155 (replaced) [pdf, other]
Title: Controllable electron spin dephasing due to phonon state distinguishability in a coupled quantum dot system
Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)
[34]  arXiv:1707.06200 (replaced) [pdf, ps, other]
Title: Nonlocal games, synchronous correlations, and Bell inequalities
Subjects: Quantum Physics (quant-ph)
[35]  arXiv:1707.08730 (replaced) [pdf, ps, other]
Title: A Quantum Approach to Subset-Sum and Similar Problems