249 research outputs found
Analytical solution of the time evolution of an entangled electron spin pair in a double quantum dot nanostructure
Using master equations we present an analytical solution of the time
evolution of an entangled electron spin pair which can occupy 36 different
quantum states in a double quantum dot nanostructure. This solution is exact
given a few realistic assumptions and takes into account relaxation and
decoherence rates of the electron spins as phenomenological parameters. Our
systematic method of solving a large set of coupled differential equations is
straightforward and can be used to obtain analytical predictions of the quantum
evolution of a large class of complex quantum systems, for which until now
commonly numerical solutions have been sought.Comment: 23 pages, 3 figure
An analytical decomposition protocol for optimal implementation of two-qubit entangling gates
This paper addresses the question how to implement a desired two-qubit gate U
using a given tunable two-qubit entangling interaction H_int. We present a
general method which is based on the K_1 A K_2 decomposition of unitary
matrices in SU(4) to calculate analytically the smallest number of two-qubit
gates U_int [based on H_int] and single-qubit rotations, and the explicit
sequence of these operations that are required to implement U. We illustrate
our protocol by calculating the implementation of (1) the transformation from
standard basis to Bell basis, (2) the CNOT gate, and (3) the quantum Fourier
transform for two kinds of interaction - Heisenberg exchange interaction and
quantum inductive coupling - and discuss the relevance of our results for
solid-state qubits.Comment: 16 pages, published versio
Detecting entanglement of two electron spin qubits with witness operators
We propose a scheme for detecting entanglement between two electron spin
qubits in a double quantum dot using an entanglement witness operator. We first
calculate the optimal configuration of the two electron spins, defined as the
position in the energy level spectrum where, averaged over the nuclear spin
distribution, 1) the probability to have two separated electrons, and 2) the
degree of entanglement of the quantum state quantified by the concurrence are
both large. Using a density matrix approach, we then calculate the evolution of
the expectation value of the witness operator for the two-spin singlet state,
taking into account the effect of decoherence due to quantum charge
fluctuations modeled as a boson bath. We find that, for large interdot
coupling, it is possible to obtain a highly entangled and robust ground state.Comment: 4 pages, 3 figure
Energy Spectrum and Exact Cover in an Extended Quantum Ising Model
We investigate an extended version of the quantum Ising model which includes
beyond-nearest neighbour interactions and an additional site-dependent
longitudinal magnetic field. Treating the interaction exactly and using
perturbation theory in the longitudinal field, we calculate the energy spectrum
and find that the presence of beyond-nearest-neighbour interactions enhances
the minimal gap between the ground state and the first excited state,
irrespective of the nature of decay of these interactions along the chain. The
longitudinal field adds a correction to this gap that is independent of the
number of qubits. We discuss the application of our model to implementing
specific instances of 3-satisfiability problems (Exact Cover) and make a
connection to a chain of flux qubits.Comment: 9 pages, 3 figures, published versio
Detecting entanglement using a double quantum dot turnstile
We propose a scheme based on using the singlet ground state of an electron
spin pair in a double quantum dot nanostructure as a suitable set-up for
detecting entanglement between electron spins via the measurement of an optimal
entanglement witness. Using time-dependent gate voltages and magnetic fields
the entangled spins are separated and coherently rotated in the quantum dots
and subsequently detected at spin-polarized quantum point contacts. We analyze
the coherent time evolution of the entangled pair and show that by counting
coincidences in the four exits an entanglement test can be done. This set-up is
close to present-day experimental possibilities and can be used to produce
pairs of entangled electrons ``on demand''.Comment: 5 pages, 2 figures - published versio
Superluminal Optical Phase Conjugation: Pulse Reshaping and Instability
We theoretically investigate the response of optical phase conjugators to
incident probe pulses. In the stable (sub-threshold) operating regime of an
optical phase conjugator it is possible to transmit probe pulses with a
superluminally advanced peak, whereas conjugate reflection is always
subluminal. In the unstable (above-threshold) regime, superluminal response
occurs both in reflection and in transmission, at times preceding the onset of
exponential growth due to the instability.Comment: 9 pages, 6 figures, RevTex, to appear in Phys. Rev.
Multiparticle entanglement under the influence of decoherence
We present a method to determine the decay of multiparticle quantum
correlations as quantified by the geometric measure of entanglement under the
influence of decoherence. With this, we compare the robustness of entanglement
in GHZ-, cluster-, W- and Dicke states of four qubits and show that the Dicke
state is most robust. Finally, we determine the geometric measure analytically
for decaying GHZ and cluster states of an arbitrary number of qubits.Comment: 5 pages, 3 figures, v2: final version, to appear as a Rapid
Communication in PR
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