887 research outputs found
Degenerate Quantum Codes for Pauli Channels
A striking feature of quantum error correcting codes is that they can
sometimes be used to correct more errors than they can uniquely identify. Such
degenerate codes have long been known, but have remained poorly understood. We
provide a heuristic for designing degenerate quantum codes for high noise
rates, which is applied to generate codes that can be used to communicate over
almost any Pauli channel at rates that are impossible for a nondegenerate code.
The gap between nondegenerate and degenerate code performance is quite large,
in contrast to the tiny magnitude of the only previous demonstration of this
effect. We also identify a channel for which none of our codes outperform the
best nondegenerate code and show that it is nevertheless quite unlike any
channel for which nondegenerate codes are known to be optimal.Comment: Introduction changed to give more motivation and background. Figure 1
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The linearization of the Kodama state
We study the question of whether the linearization of the Kodama state around
classical deSitter spacetime is normalizable in the inner product of the theory
of linearized gravitons on deSitter spacetime. We find the answer is no in the
Lorentzian theory. However, in the Euclidean theory the corresponding
linearized Kodama state is delta-functional normalizable. We discuss whether
this result invalidates the conjecture that the full Kodama state is a good
physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte
Nonlinear spectroscopy of superconducting anharmonic resonators
We formulate a model for the steady state response of a nonlinear quantum
oscillator structure, such as those used in a variety of superconducting qubit
experiments, when excited by a steady, but not necessarily small, ac tone. We
show that this model can be derived directly from a circuit description of some
recent qubit experiments in which the state of the qubit is read out directly,
without a SQUID magnetometer. The excitation profile has a rich structure
depending on the detuning of the tone from the small-signal resonant frequency,
on the degree of damping, and on the excitation amplitude. We explore two
regions in detail: First, at high damping there is a trough in the excitation
response as a function of detuning, near where the classical Duffing
bifurcation occurs. This trough has been understood as a classical interference
between two metastable responses with opposite phase. We use Wigner function
studies to show that while this picture is roughly correct, there are also more
quantum mechanical aspects to this feature. Second, at low damping we study the
emergence of sharp, discrete spectral features from a continuum response. We
show that these the structures, associated with discrete transitions between
different excited-state eigenstates of the oscillator, provide an interesting
example of a quantum Fano resonance. The trough in the Fano response evolves
continuously from the "classical" trough at high damping
Security Trade-offs in Ancilla-Free Quantum Bit Commitment in the Presence of Superselection Rules
Security trade-offs have been established for one-way bit commitment in
quant-ph/0106019. We study this trade-off in two superselection settings. We
show that for an `abelian' superselection rule (exemplified by particle
conservation) the standard trade-off between sealing and binding properties
still holds. For the non-abelian case (exemplified by angular momentum
conservation) the security trade-off can be more subtle, which we illustrate by
showing that if the bit-commitment is forced to be ancilla-free an
asymptotically secure quantum bit commitment is possible.Comment: 7 pages Latex; v2 has 8 pages and additional references and
clarifications, this paper is to appear in the New Journal of Physic
Optimal universal and state-dependent quantum cloning
We establish the best possible approximation to a perfect quantum cloning machine that produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two nonorthogonal states and discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive an upper bound on the quantum capacity of the depolarizing quantum channel
Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
We report new results and generalizations of our work on unextendible product
bases (UPB), uncompletable product bases and bound entanglement. We present a
new construction for bound entangled states based on product bases which are
only completable in a locally extended Hilbert space. We introduce a very
useful representation of a product basis, an orthogonality graph. Using this
representation we give a complete characterization of unextendible product
bases for two qutrits. We present several generalizations of UPBs to arbitrary
high dimensions and multipartite systems. We present a sufficient condition for
sets of orthogonal product states to be distinguishable by separable
superoperators. We prove that bound entangled states cannot help increase the
distillable entanglement of a state beyond its regularized entanglement of
formation assisted by bound entanglement.Comment: 24 pages RevTex, 15 figures; appendix removed, several small
corrections, to appear in Comm. Math. Phy
Simulating quantum operations with mixed environments
We study the physical resources required to implement general quantum
operations, and provide new bounds on the minimum possible size which an
environment must be in order to perform certain quantum operations. We prove
that contrary to a previous conjecture, not all quantum operations on a
single-qubit can be implemented with a single-qubit environment, even if that
environment is initially prepared in a mixed state. We show that a mixed
single-qutrit environment is sufficient to implement a special class of
operations, the generalized depolarizing channels.Comment: 4 pages Revtex + 1 fig, pictures at
http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small correction
Unification of gravity, gauge fields, and Higgs bosons
We consider a diffeomorphism invariant theory of a gauge field valued in a
Lie algebra that breaks spontaneously to the direct sum of the spacetime
Lorentz algebra, a Yang-Mills algebra, and their complement. Beginning with a
fully gauge invariant action -- an extension of the Plebanski action for
general relativity -- we recover the action for gravity, Yang-Mills, and Higgs
fields. The low-energy coupling constants, obtained after symmetry breaking,
are all functions of the single parameter present in the initial action and the
vacuum expectation value of the Higgs.Comment: 12 pages, no figures. v2 minor correction
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