1,032 research outputs found
Perturbative expansions for the fidelities and spatially correlated dissipation of quantum bits
We construct generally applicable short-time perturbative expansions for some
fidelities, such as the input-output fidelity, the entanglement fidelity, and
the average fidelity. Successive terms of these expansions yield characteristic
times for the damping of the fidelities involving successive powers of the
Hamiltonian. The second-order results, which represent the damping rates of the
fidelities, are extensively discussed. As an interesting application of these
expansions, we use them to study the spatially-correlated dissipation of
quantum bits. Spatial correlations in the dissipation are described by a
correlation function. Explicit conditions are derived for independent
decoherence and for collective decoherence.Comment: Minor changes in discussion
Incomplete pure dephasing of N-qubit entangled W states
We consider qubits in a linear arrangement coupled to a bosonic field which
acts as a quantum heat bath and causes decoherence. By taking the spatial
separation of the qubits explicitly into account, the reduced qubit dynamics
acquires an additional non-Markovian element. We investigate the time evolution
of an entangled many-qubit W state, which for vanishing qubit separation
remains robust under pure dephasing. For finite separation, by contrast, the
dynamics is no longer decoherence-free. On the other hand, spatial noise
correlations may prevent a complete dephasing. While a standard Bloch-Redfield
master equation fails to describe this behavior even qualitatively, we propose
instead a widely applicable causal master equation. Here we employ it to
identify and characterize decoherence-poor subspaces. Consequences for quantum
error correction are discussed.Comment: 14 pages, 6 figures, revised version, to appear in Phys. Rev.
Spatial noise filtering through error correction for quantum sensing
Quantum systems can be used to measure various quantities in their
environment with high precision. Often, however, their sensitivity is limited
by the decohering effects of this same environment. Dynamical decoupling
schemes are widely used to filter environmental noise from signals, but their
performance is limited by the spectral properties of the signal and noise at
hand. Quantum error correction schemes have therefore emerged as a
complementary technique without the same limitations. To date, however, they
have failed to correct the dominant noise type in many quantum sensors, which
couples to each qubit in a sensor in the same way as the signal. Here we show
how quantum error correction can correct for such noise, which dynamical
decoupling can only partially address. Whereas dynamical decoupling exploits
temporal noise correlations in signal and noise, our scheme exploits spatial
correlations. We give explicit examples in small quantum devices and
demonstrate a method by which error-correcting codes can be tailored to their
noise.Comment: 8 pages, 2 figures, RevTeX 4.1. v2: Updated to match published
versio
Spin entanglement, decoherence and Bohm's EPR paradox
We obtain criteria for entanglement and the EPR paradox
for spin-entangled particles and analyse the effects of decoherence caused
by absorption and state purity errors. For a two qubit photonic state,
entanglement can occur for all transmission efficiencies. In this case,
the state preparation purity must be above a threshold value. However,
Bohm’s spin EPR paradox can be achieved only above a critical level of
loss. We calculate a required efficiency of 58%, which appears achievable
with current quantum optical technologies. For a macroscopic number of
particles prepared in a correlated state, spin entanglement and the EPR
paradox can be demonstrated using our criteria for efficiencies η > 1/3
and η > 2/3 respectively. This indicates a surprising insensitivity to loss
decoherence, in a macroscopic system of ultra-cold atoms or photons
Sufficient condition on noise correlations for scalable quantum computing
I study the effectiveness of fault-tolerant quantum computation against
correlated Hamiltonian noise, and derive a sufficient condition for
scalability. Arbitrarily long quantum computations can be executed reliably
provided that noise terms acting collectively on k system qubits are
sufficiently weak, and decay sufficiently rapidly with increasing k and with
increasing spatial separation of the qubits.Comment: 13 pages, 1 figure. (v2) Minor corrections and clarification
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