Perfect transfer of m-qubit GHZ states (original) (raw)

Optimal transfer of a d -level quantum state over pseudo-distance-regular networks

Journal of Physics A: Mathematical and Theoretical, 2008

In the previous work (Jafarizadeh and Sufiani 2008 Phys. Rev. A 77 022315), by using some techniques such as stratification and spectral distribution associated with the graphs, perfect state transfer (PST) of a qubit (spin 1/2 particle) over distance-regular spin networks was discussed. In this paper, optimal transfer of an arbitrary d-level quantum state (qudit) over antipodes of more general networks called pseudo-distance-regular networks, is investigated. In other words, by using the same spectral analysis techniques and algebraic structures of pseudo-distance-regular graphs, we give an explicit analytical formula for suitable coupling constants in the specific Hamiltonians so that the state of a particular qudit initially encoded on one site will optimally evolve into the opposite site without any dynamical control, i.e., we show how to analytically derive the parameters of the system so that optimal state transfer can be achieved. Also, for the specific form of Hamiltonians that we consider, necessary conditions in order for PST to be achieved are given. Finally, for these Hamiltonians, PST and optimal imperfect ST over some important examples of pseudo-distance regular networks are discussed.

Perfect State Transfer in Quantum Spin Networks

Physical Review Letters, 2004

We propose a class of qubit networks that admit perfect transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2 log 3 N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.

Generating a GHZ state in 2m-qubit spin network

Journal of Statistical Mechanics-theory and Experiment, 2011

We consider a pure 2m-qubit initial state to evolve under a particular quantum me- chanical spin Hamiltonian, which can be written in terms of the adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques such as spectral dis- tribution and strati?cation associated with the graphs, employed in [1, 2], a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an explicit formula is given for the suitable coupling strengths of the hamiltonian, so that a maximally entangled state can be generated between antipodes of the network. By using some known multipartite entanglement measures, the amount of the entanglement of the ?nal evolved state is calculated, and ?nally two examples of four qubit and six qubit states are considered in details.

Perfect transfer of arbitrary states in quantum spin networks

Physical Review A, 2005

An important task in quantum-information processing is the transfer of quantum states from one location A to another location B. In a quantum-communication scenario this is rather explicit, since the goal is the communication between distant parties A and B eg, by means of photon transmission. Equally, in the interior of quantum computers good communication between different parts of the system is essential. The need is thus to transfer quantum states and generate entanglement between different regions contained within the system. ...

Quantum-state transfer in imperfect artificial spin networks

Physical Review A, 2005

High-fidelity quantum computation and quantum state transfer are possible in short spin chains. We exploit a system based on a dispersive qubit-boson interaction to mimic XY coupling. In this model, the usually assumed nearest-neighbors coupling is no more valid: all the qubits are mutually coupled. We analyze the performances of our model for quantum state transfer showing how pre-engineered coupling rates allow for nearly optimal state transfer. We address a setup of superconducting qubits coupled to a microstrip cavity in which our analysis may be applied.

Transfer of arbitrary two-qubit states via a spin chain

Physical Review A, 2015

We investigate the fidelity of the quantum state transfer (QST) of two qubits by means of an arbitrary spin-1 2 network, on a lattice of any dimensionality. Under the assumptions that the network Hamiltonian preserves the magnetization and that a fully polarized initial state is taken for the lattice, we obtain a general formula for the average fidelity of the two qubits QST, linking it to the oneand two-particle transfer amplitudes of the spin-excitations among the sites of the lattice. We then apply this formalism to a 1D spin chain with XX-Heisenberg type nearest-neighbour interactions adopting a protocol that is a generalization of the single qubit one proposed in Ref. [Phys. Rev. A 87, 062309 (2013)]. We find that a high-quality two qubit QST can be achieved provided one can control the local fields at sites near the sender and receiver. Under such conditions, we obtain an almost perfect transfer in a time that scales either linearly or, depending on the spin number, quadratically with the length of the chain.

On quantum perfect state transfer in weighted join graphs

2009

We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove include: • The join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al. [9] where the regular graph is a complete graph or a complete graph with a missing link. In contrast, the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. This implies that adding weights in a complete bipartite graph do not help in achieving perfect state transfer. • A Hamming graph has perfect state transfer between each pair of its vertices. This is obtained using a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on the hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes. This generalizes results of Bernasconi et al. [5] and Moore and Russell [14]. Our techniques rely heavily on the spectral properties of graphs built using the join and Cartesian product operators.

Perfect state transfer via quantum probability theory

Quantum Information Processing, 2013

The transfer of quantum states has played an important role in quantum information processing. In fact, transfer of quantum states from point A to B with unit fidelity is very important for us and we focus on this case. In recent years, in represented works, they designed Hamiltonian in a way that a mirror symmetry creates with with respect to network center. In this paper, we stratify the spin network with respect to an arbitrary vertex of the spin network o then we design coupling coefficient in a way to create a mirror symmetry in Hamiltonian with respect to center. By using this Hamiltonian and represented approach, initial state that have been encoded on the first vertex in suitable

Perfect state transfer in networks of arbitrary topology and coupling configuration

Physical Review A, 2007

A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians which may provide solution to this problem. In a first attempt to give a classification of them we investigate their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations.

Pretty good state transfer in qubit chains—The Heisenberg Hamiltonian

Journal of Mathematical Physics

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits there is pretty good state transfer between the nodes at the j-th and (n−j +1)-th position if n is prime congruent to 1 modulo 4 or a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory.