7,417 research outputs found
Super Quantum Discord with Weak Measurements
Weak measurements cause small change to quantum states, thereby opening up
the possibility of new ways of manipulating and controlling quantum systems. We
ask, can weak measurements reveal more quantum correlation in a composite
quantum state? We prove that the weak measurement induced quantum discord,
called as the "super quantum discord", is always larger than the quantum
discord captured by the strong measurement. Moreover, we prove the monotonicity
of the super quantum discord as a function of the measurement strength. We find
that unlike the normal quantum discord, for pure entangled states, the super
quantum discord can exceed the quantum entanglement. Our result shows that the
notion of quantum correlation is not only observer dependent but also depends
on how weakly one perturbs the composite system.Comment: Latex, 5 pages, 2 Figs, Monotonicity of the super discord with the
measurement strength is included. Application to the entropic uncertainty
relation will be reported separatel
Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity
The work identifies the first lattice decoding solution that achieves, in the
general outage-limited MIMO setting and in the high-rate and high-SNR limit,
both a vanishing gap to the error-performance of the (DMT optimal) exact
solution of preprocessed lattice decoding, as well as a computational
complexity that is subexponential in the number of codeword bits. The proposed
solution employs lattice reduction (LR)-aided regularized (lattice) sphere
decoding and proper timeout policies. These performance and complexity
guarantees hold for most MIMO scenarios, all reasonable fading statistics, all
channel dimensions and all full-rate lattice codes.
In sharp contrast to the above manageable complexity, the complexity of other
standard preprocessed lattice decoding solutions is shown here to be extremely
high. Specifically the work is first to quantify the complexity of these
lattice (sphere) decoding solutions and to prove the surprising result that the
complexity required to achieve a certain rate-reliability performance, is
exponential in the lattice dimensionality and in the number of codeword bits,
and it in fact matches, in common scenarios, the complexity of ML-based
solutions. Through this sharp contrast, the work was able to, for the first
time, rigorously quantify the pivotal role of lattice reduction as a special
complexity reducing ingredient.
Finally the work analytically refines transceiver DMT analysis which
generally fails to address potentially massive gaps between theory and
practice. Instead the adopted vanishing gap condition guarantees that the
decoder's error curve is arbitrarily close, given a sufficiently high SNR, to
the optimal error curve of exact solutions, which is a much stronger condition
than DMT optimality which only guarantees an error gap that is subpolynomial in
SNR, and can thus be unbounded and generally unacceptable in practical
settings.Comment: 16 pages - submission for IEEE Trans. Inform. Theor
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