858 research outputs found
An NMR Analog of the Quantum Disentanglement Eraser
We report the implementation of a three-spin quantum disentanglement eraser
on a liquid-state NMR quantum information processor. A key feature of this
experiment was its use of pulsed magnetic field gradients to mimic projective
measurements. This ability is an important step towards the development of an
experimentally controllable system which can simulate any quantum dynamics,
both coherent and decoherent.Comment: Four pages, one figure (RevTeX 2.1), to appear in Physics Review
Letter
Incoherent Noise and Quantum Information Processing
Incoherence in the controlled Hamiltonian is an important limitation on the
precision of coherent control in quantum information processing. Incoherence
can typically be modelled as a distribution of unitary processes arising from
slowly varying experimental parameters. We show how it introduces artifacts in
quantum process tomography and we explain how the resulting estimate of the
superoperator may not be completely positive. We then go on to attack the
inverse problem of extracting an effective distribution of unitaries that
characterizes the incoherence via a perturbation theory analysis of the
superoperator eigenvalue spectra.Comment: 15 pages, 5 figures, replaced with future JCP published versio
Subsystem Pseudo-pure States
A critical step in experimental quantum information processing (QIP) is to
implement control of quantum systems protected against decoherence via
informational encodings, such as quantum error correcting codes, noiseless
subsystems and decoherence free subspaces. These encodings lead to the promise
of fault tolerant QIP, but they come at the expense of resource overheads.
Part of the challenge in studying control over multiple logical qubits, is
that QIP test-beds have not had sufficient resources to analyze encodings
beyond the simplest ones. The most relevant resources are the number of
available qubits and the cost to initialize and control them. Here we
demonstrate an encoding of logical information that permits the control over
multiple logical qubits without full initialization, an issue that is
particularly challenging in liquid state NMR. The method of subsystem
pseudo-pure state will allow the study of decoherence control schemes on up to
6 logical qubits using liquid state NMR implementations.Comment: 9 pages, 1 Figur
Principles of Control for Decoherence-Free Subsystems
Decoherence-Free Subsystems (DFS) are a powerful means of protecting quantum
information against noise with known symmetry properties. Although Hamiltonians
theoretically exist that can implement a universal set of logic gates on DFS
encoded qubits without ever leaving the protected subsystem, the natural
Hamiltonians that are available in specific implementations do not necessarily
have this property. Here we describe some of the principles that can be used in
such cases to operate on encoded qubits without losing the protection offered
by the DFS. In particular, we show how dynamical decoupling can be used to
control decoherence during the unavoidable excursions outside of the DFS. By
means of cumulant expansions, we show how the fidelity of quantum gates
implemented by this method on a simple two-physical-qubit DFS depends on the
correlation time of the noise responsible for decoherence. We further show by
means of numerical simulations how our previously introduced "strongly
modulating pulses" for NMR quantum information processing can permit
high-fidelity operations on multiple DFS encoded qubits in practice, provided
that the rate at which the system can be modulated is fast compared to the
correlation time of the noise. The principles thereby illustrated are expected
to be broadly applicable to many implementations of quantum information
processors based on DFS encoded qubits.Comment: 12 pages, 7 figure
A Note on the correspondence between Qubit Quantum Operations and Special Relativity
We exploit a well-known isomorphism between complex hermitian
matrices and , which yields a convenient real vector
representation of qubit states. Because these do not need to be normalized we
find that they map onto a Minkowskian future cone in , whose
vertical cross-sections are nothing but Bloch spheres. Pure states are
represented by light-like vectors, unitary operations correspond to special
orthogonal transforms about the axis of the cone, positive operations
correspond to pure Lorentz boosts. We formalize the equivalence between the
generalized measurement formalism on qubit states and the Lorentz
transformations of special relativity, or more precisely elements of the
restricted Lorentz group together with future-directed null boosts. The note
ends with a discussion of the equivalence and some of its possible
consequences.Comment: 6 pages, revtex, v3: revised discussio
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