Robustness of Highly Entangled Multi-Qubit States Under Decoherence

We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |GHZ> state.Comment: 16 pages, 3 figures. Changes in Sec.

Efficient generation of random multipartite entangled states using time optimal unitary operations

We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.Comment: 5 pages, 2 figures. New title, improved explanation of the algorithm. To appear in Phys. Rev.

The Mariner 5 flight path and its determination from tracking data

Mariner 5 flight path and its determination from tracking dat

Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also explored.Comment: 24 pages, 3 figure

A genuine maximally seven-qubit entangled state

Contrary to A.Borras et al.'s [1] conjecture, a genuine maximally seven-qubit entangled state is presented. We find a seven-qubit state whose marginal density matrices for subsystems of 1,2- qubits are all completely mixed and for subsystems of 3-qubits is almost completely mixed

Brachistochrone of Entanglement for Spin Chains

We analytically investigate the role of entanglement in time-optimal state evolution as an appli- cation of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly cou- pled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entan- glement plays a role for W and GHZ initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.Comment: 9 pages, 4 figure

Quantum teleportation and state sharing using a genuinely entangled six qubit state

The usefulness of the genuinely entangled six qubit state that was recently introduced by Borras et al. is investigated for the quantum teleportation of an arbitrary three qubit state and for quantum state sharing (QSTS) of an arbitrary two qubit state. For QSTS, we explicitly devise two protocols and construct sixteen orthogonal measurement basis which can lock an arbitrary two qubit information between two parties.Comment: 6 pages, 7 table

Generalized Criterion of Maximally Multi-Qubit Entanglement

We first present a generalized criterion for maximally entangled states of 2, 3, 4, 5, 6, 8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine eight-qubit maximally entangle state is obtained. For the 4, 7 and 8 qubits system in which no maximally multi-qubit entangled states (MMES) is thought to exist before, we find that the proved and most suspected MMESes, are not completely mixed in subsystem with a critical-number qubits, below which the subsystems are all completely mixed. We believe that the new criterion and MMES can play important role in quantum information technology, such as the teleportation and dense coding

Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

We give analytical solutions for the time-optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an Ising Hamiltonian interaction with equal coupling $J$ plus a local magnetic field acting on the intermediate qubit. The energy available is fixed, but we relax the standard assumption of instantaneous unitary operations acting on single qubits. The time required for performing an entangling gate which is equivalent, modulo local unitary operations, to the $\mathrm{CNOT}(1, 3)$ between the indirectly coupled qubits 1 and 3 is $T=\sqrt{3/2} J^{-1}$, i.e. faster than a previous estimate based on a similar Hamiltonian and the assumption of local unitaries with zero time cost. Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space of qubit 3 shows that the time-optimal synthesis of the $\mathrm{CNOT}^{\pm}(1, 3)$ (which acts as the identity when the control qubit 1 is in the state $\ket{0}$, while if the control qubit is in the state $\ket{1}$ the target qubit 3 is flipped as $\ket{\pm}\rightarrow \ket{\mp}$) also requires the same time $T$.Comment: 9 pages; minor modification

Highly entangled multi-qubit states with simple algebraic structure

Recent works by Brown et al and Borras et al have explored numerical optimisation procedures to search for highly entangled multi-qubit states according to some computationally tractable entanglement measure. We present an alternative scheme based upon the idea of searching for states having not only high entanglement but also simple algebraic structure. We report results for 4, 5, 6, 7 and 8 qubits discovered by this approach, showing that many of such states do exist. In particular, we find a maximally entangled 6-qubit state with an algebraic structure simpler than the best results known so far. For the case of 7, we discover states with high, but not maximum, entanglement and simple structure, as well as other desirable properties. Some preliminary results are shown for the case of 8 qubits.Comment: 15 pages, 1 figur