Asymmetric quantum telecloning of d-level systems and broadcasting of entanglement to different locations using the many-to-many communication protocol
We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to M>N receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local 1->2 optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal optimal universal asymmetric cloning machine and we show that the symmetric machine optimally copies the entanglement. The many-to-many teleportation scheme is applied in order to distribute entanglement shared between two observers to two pairs of spatially separated observers.
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.
We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as post-measurement states. Moreover, such entropy is an upper bound to the average bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic evaluation of the spectrum of $M$-body DMs in some strongly correlated fermionic states is also provided.
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement and show there is a total order for multipartite quantum states in this framework. We also present new results on hypothesis testing of correlated sources and give further evidence on the existence of NPPT bound entanglement. In the second part, we study the potential as well as the limitations of a quantum computer for calculating properties of many-body systems. First we analyse the usefulness of quantum computation to calculate additive approximations to partition functions and spectral densities of local Hamiltonians. We then show that the determination of ground state energies of local Hamiltonians with an inverse polynomial spectral gap is QCMA-hard. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. We analyze the realization of paradigmatic condensed matter Hamiltonians in arrays of coupled microcavities, such as the Bose-Hubbard and the anisotropic Heisenberg models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Greens function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional $J_1-J_2$ Heisenberg model. The method is general and can be extended to other variational forms.
Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational tool to simulate quantum systems consisting of many particles, a very demanding computational task. In this paper, we present a novel ab-initio approach to solve the many-body problem for bosonic systems by evolving a system of one-particle wavefunctions representing pilot waves that guide the Bohmian trajectories of the quantum particles. In this approach, quantum entanglement effects arise due to the interactions between different configurations of Bohmian particles evolving simultaneously. The method is used to study the breathing dynamics and ground state properties in a system of interacting bosons.
Iulia Ghiu KTH
,Kista
,Sweden
.
(2003)
.
"Asymmetric quantum telecloning of d-level systems and broadcasting of entanglement to different locations using the many-to-many communication protocol"
.
Iulia Ghiu
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