12,643 research outputs found
Extremal RN/CFT in Both Hands Revisited
We study RN/CFT correspondence for four dimensional extremal
Reissner-Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating
black hole and make a geometric regularization of the 5d space-time. Both hands
central charges are obtained correctly at the same time by Brown-Henneaux
technique.Comment: 10 pages, no figur
The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes
Quantum error-correcting codes are used to protect quantum information from
decoherence. A raw state is mapped, by an encoding circuit, to a codeword so
that the most likely quantum errors from a noisy quantum channel can be removed
after a decoding process.
A good encoding circuit should have some desired features, such as low depth,
few gates, and so on. In this paper, we show how to practically implement an
encoding circuit of gate complexity for an
quantum stabilizer code with the help of pairs of maximally-entangled
states. For the special case of an stabilizer code with , the
encoding complexity is , which is previously known to be
. For this suggests that the benefits from shared
entanglement come at an additional cost of encoding complexity.
Finally we discuss decoding of entanglement-assisted quantum stabilizer codes
and extend previously known computational hardness results on decoding quantum
stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information
Theory (ISIT2019
On the Anti-Wishart distribution
We provide the probability distribution function of matrix elements each of
which is the inner product of two vectors.
The vectors we are considering here are independently distributed but not
necessarily Gaussian variables.
When the number of components M of each vector is greater than the number of
vectors N, one has a symmetric matrix.
When and the components of each vector are independent Gaussian
variables, the distribution function of the matrix elements was
obtained by Wishart in 1928.
When N > M, what we called the ``Anti-Wishart'' case, the matrix elements are
no longer completely independent because the true degrees of freedom becomes
smaller than the number of matrix elements. Due to this singular nature,
analytical derivation of the probability distribution function is much more
involved than the corresponding Wishart case. For a class of general random
vectors, we obtain the analytical distribution function in a closed form, which
is a product of various factors and delta function constraints, composed of
various determinants. The distribution function of the matrix element for the
case with the same class of random vectors is also obtained as a
by-product. Our result is closely related to and should be valuable for the
study of random magnet problem and information redundancy problem.Comment: to appear in Physica
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