arXiv subjects

Tim Byrnes

Publications and source records attributed to Tim Byrnes.

At least 91 records · Page 5Linked to original sources

arXiv2018

Flux unwinding in the lattice Schwinger model

We study the dynamics of the massive Schwinger model on a lattice using exact diagonalization. When periodic boundary conditions are imposed, analytic arguments indicate that a non-zero electric flux in the initial state can "unwind" and decrease to a minimum value equal to minus its initial value, due to the effects of a pair of charges that repeatedly traverse the spatial circle. Our numerical results support the existence of this flux unwinding phenomenon, both for initial states containing a charged pair inserted by hand, and when the charges are produced by Schwinger pair production. We also study boundary conditions where charges are confined to an interval and flux unwinding cannot occur, and the massless limit, where our results agree with the predictions of the bosonized description of the Schwinger model.

hep-th↗

arXiv2018

Adiabatic entangling gate of Bose-Einstein condensates based on the minimum function

A scheme is presented to perform an entangling gate between two atomic ensembles or Bose-Einstein condensates in a optical cavity with a common optical mode. The method involves using a generalized Stimulated Raman Adiabatic Passage (STIRAP) to adiabatically evolve the ground state. We show that dark states exist for any atom number within the cavities, and find that the operation produces an unusual type of evolution where the minimum of the number of atoms between two levels transitions to another state. This produces a unconventional type of entangling Hamiltonian which creates a phase depending on the minimum operation. We analyze its reliability under a variety of conditions ranging from the ideal decoherence-free case to that including photon loss and spontaneous emission. Ways of combating decoherence are analyzed and the amount of entanglement that is generated is calculated.

cond-mat.quant-gas↗

arXiv2018

Split spin-squeezed Bose-Einstein Condensates

We investigate and model the behaviour of split spin-squeezed Bose-Einstein condensates (BECs) system. In such a system, a spin-polarized BEC is first squeezed using a $ (S^z)^2 $ interaction, then are split into two separate clouds. After the split, we consider that the particle number in each cloud collapses to a fixed number. We show that this procedure is equivalent to applying an interaction corresponding to squeezing each cloud individually plus an entangling operation. We analyse the system's entanglement properties and show that it can be detected using correlation-based entanglement criteria. The nature of the states are illustrated by Wigner functions and have the form of a correlated squeezed state. The conditional Wigner function shows high degrees of non-classicality for dimensionless squeezing times beyond $ 1/\sqrt{N} $, where $N$ is the number of particles per BEC.

quant-ph↗

arXiv2018

Non-equilibrium time dynamics of genetic evolution

Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, examination of the time-dependent non-equilibrium dynamics has been less studied. In this paper we first derive a generalized master equation in the genotype space for diploid organisms incorporating the processes of selection, mutation, recombination, and reproduction. The master equation is defined in terms of continuous time and can handle an arbitrary number of gene loci and alleles, and can be defined in terms of an absolute population or probabilities. We examine and analytically solve several prototypical cases which illustrate the interplay of the various processes and discuss the timescales of their evolution. The entropy production during the evolution towards steady state is calculated and we find that it agrees with predictions from non-equilibrium statistical mechanics where it is large when the population distribution evolves towards a more viable genotype. The stability of the non-equilibrium steady state is confirmed using the Glansdorff-Prigogine criterion.

q-bio.PE↗

arXiv2018

Generalized framework for applying the Kelly criterion to stock markets

We develop a general framework for applying the Kelly criterion to stock markets. By supplying an arbitrary probability distribution modeling the future price movement of a set of stocks, the Kelly fraction for investing each stock can be calculated by inverting a matrix involving only first and second moments. The framework works for one or a portfolio of stocks and the Kelly fractions can be efficiently calculated. For a simple model of geometric Brownian motion of a single stock we show that our calculated Kelly fraction agrees with existing results. We demonstrate that the Kelly fractions can be calculated easily for other types of probabilities such as the Gaussian distribution and correlated multivariate assets.

q-fin.PM↗

arXiv2018

Covariance matrix entanglement criterion for an arbitrary set of operators

We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by performing a partial transposition on the operators. The method is highly efficient and versatile in the sense that the set of measurement operators can be freely chosen, do not need to be complete, and there is no constraint on the commutation relations. The method is particularly suited for systems with higher dimensionality since the computations do not scale with the dimension of the Hilbert space rather they scale with the number of chosen observables which can always be kept small. We illustrate the approach by examining the entanglement between two spin ensembles, and show that it detects entanglement in a basis independent way.

quant-ph↗

arXiv2018

A loophole-free Wheeler-delayed-choice experiment

Wheeler's delayed-choice experiment investigates the indeterminacy of wave-particle duality and the role played by the measurement apparatus in quantum theory. Due to the inconsistency with classical physics, it has been generally believed that it is not possible to reproduce the delayed-choice experiment using a hidden variable theory. Recently, it was shown that this assumption was incorrect, and in fact Wheeler's delayed-choice experiment can be explained by a causal two dimensional hidden-variable theory [R. Chaves, G. B. Lemos, and J. Pienaar, Phys. Rev. Lett. 120, 190401 (2018)]. Here, we carry out an experiment of a device-independent delayed-choice experiment using photon states that are space-like separated, and demonstrate a loophole-free version of the delayed-choice protocol that is consistent with quantum theory but inconsistent with any causal two-dimensional hidden variable theory. This salvages Wheeler's thought experiment and shows that causality can be used to test quantum theory in a complementary way to the Bell and Leggett-Garg tests.

quant-ph↗

arXiv2018

Basis-independent quantum coherence and its distribution

We analyze a basis-independent definition of quantum coherence. The maximally mixed state is used as the reference state, which allows for a way of defining coherence that is invariant under arbitrary unitary transformations. The basis-independent approach is applied to finding the distri- bution of the coherence within a multipartite system, where the contributions due to correlations between the subsystems and within each subsystem are isolated. The use of the square root of the Jensen-Shannon divergence allows for inequality relations to be derived between these quantities, giving a geometrical picture within the Hilbert space of the system. We describe the relationship between the basis-independent and the basis-dependent approaches, and argue that many advan- tages exist for the former method. The formalism is illustrated with several numerical examples which show that the states can be characterized in a simple and effective manner.

quant-ph↗

arXiv2018

Fingering instabilities and pattern formation in a two-component dipolar Bose-Einstein condensate

We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimensional approximation are performed, and the characteristic lengths of the domains are estimated analytically. Patterns resembling those in magnetic classical fluids are modulated when the number ratio of atoms, the trap ratio of the external potential, or tilted polarization with respect to the z direction is varied.

cond-mat.quant-gas↗

arXiv2018

Bitcoin and quantum computing

Bitcoin is a digital currency and payment system based on classical cryptographic technologies which works without a central administrator such as in traditional currencies. It has long been questioned what the impact of quantum computing would be on Bitcoin, and cryptocurrencies in general. Here, we analyse three primary directions that quantum computers might have an impact in: mining, security, and forks. We find that in the near-term the impact of quantum computers appear to be rather small for all three directions. The impact of quantum computers would require considerably larger number of qubits and breakthroughs in quantum algorithms to reverse existing hash functions.

quant-ph↗

arXiv2018

Generalized Grover's algorithm for multiple phase inversion states

Grover's algorithm is a quantum search algorithm that proceeds by repeated applications of the Grover operator and the Oracle until the state evolves to one of the target states. In the standard version of the algorithm, the Grover operator inverts the sign on only one state. Here we provide an exact solution to the problem of performing Grover's search where the Grover operator inverts the sign on N states. We show the underlying structure in terms of the eigenspectrum of the generalized Hamiltonian, and derive an appropriate initial state to perform the Grover evolution. This allows us to use the quantum phase estimation algorithm to solve the search problem in this generalized case, completely bypassing the Grover algorithm altogether. We obtain a time complexity of this case of $\sqrt(D/M^α)$ where D is the search space dimension, M is the number of target states, and $α$ ~ 1, which is close to the optimal scaling.

quant-ph↗

arXiv2017

On the role of the measurement apparatus in quantum measurements

We study the extent to which the outcomes of a quantum measurement can be manipulated by changing the state of the measurement apparatus. The measurement process is modeled as decoherence induced by the experimenter, to gain knowledge about a particular system. The measurement apparatus is assumed to contain a large number of degrees of freedom, and the measurement outcomes are obtained by looking at the long interaction time limit. We study two cases which show contrasting behaviour. With a fixed axis coupling, the measurement is performed along the pointer basis with a high degree of robustness, for a wide variety of bath states. In a second model with Heisenberg interactions, the measurement outcomes can be altered considerably by changing the state of the bath.

quant-ph↗

arXiv2017

Time dynamics of quantum coherence and monogamy in a non-Markovian environment

The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantum state in terms of a coherence tuple on a multipartite state simply by examining various combinations of reservoir couplings. The effect of the environment on the shareability of quantum coherence, as defined using the monogamy of coherence, is investigated and found that the sign of the monogamy is a preserved quantity under the decoherence. We conjecture that the monogamy of coherence is a conserved property under local incoherent processes.

quant-ph↗

arXiv2017

Remote quantum clock synchronization without synchronized clocks

A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of the availability of synchronized clocks within the protocol. In general, quantum operations between two parties do not have consistent phase definitions of quantum states, which introduce an unknown systematic phase error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which are most compatible with current photon based long-distance entanglement distribution schemes. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology.

quant-ph↗

arXiv2017

Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The $σ^{z} σ^{z}$ interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and and similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.

quant-ph↗

arXiv2017

High accuracy energy formulas for the attractive two-site Bose-Hubbard model

The attractive two-site Bose-Hubbard model is studied within the framework of the analytical solution obtained by the application of Quantum Inverse Scattering Method. The structure of the ground and excited states is analyzed in terms of solutions of Bethe equations, and an approximate solution for the Bethe roots are given. This yields approximate formulas for the ground state and for the first excited state energies. The obtained formulas work with remarkable precision for a wide range of parameters of the model, and confirmed numerically. An expansion of the Bethe state vectors into a Fock space is also provided for evaluation of expectation values, although this does not have the similar accuracy to the energies.

quant-ph↗

arXiv2017

Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction

The quantum coherence of one dimensional planar spin models with the Dzyaloshinsky-Moriya interaction is investigated. The anisotropic XY model, the isotropic XX model and the transverse field model are studied in the large N-limit using the two qubit reduced density matrices and the two point correlation functions. From our investigations we find that the coherence as measured using the Jensen-Shannon divergence can be used to detect the quantum phase transitions and the quantum critical points. The derivative of coherence shows non-analytic behavior at the critical points leading to the conclusions that these transitions are of second order. Further we show that the presence of the Dzyaloshinsky-Moriya coupling suppresses the phase transition due to the residual ferromagnetism which is caused by spin canting.

quant-ph↗

arXiv2017

Highly excited exciton-polariton condensates

Exciton-polaritons are a coherent electron-hole-photon (e-h-p) system where condensation has been observed in semiconductor microcavities. In contrast to equilibrium Bose-Einstein condensation (BEC) for long lifetime systems, polariton condensates have a dynamical nonequilibrium feature owing to the similar physical structure that they have to semiconductor lasers. One of the distinguishing features of a condensate to a laser is the presence of strong coupling between the matter and photon fields. Irrespective of its equilibrium or nonequilibrium nature, exciton-polariton have been observed to maintain strong coupling. We show that by investigating high density regime of exciton-polariton condensates, the negative branch directly observed in photoluminescence. This is evidence that the present e-h-p system is still in the strong coupling regime, contrary to past results where the system reduced to standard lasing at high density.

cond-mat.quant-gas↗