3,532 research outputs found
Distilling common randomness from bipartite quantum states
The problem of converting noisy quantum correlations between two parties into
noiseless classical ones using a limited amount of one-way classical
communication is addressed. A single-letter formula for the optimal trade-off
between the extracted common randomness and classical communication rate is
obtained for the special case of classical-quantum correlations. The resulting
curve is intimately related to the quantum compression with classical side
information trade-off curve of Hayden, Jozsa and Winter. For a general
initial state we obtain a similar result, with a single-letter formula, when we
impose a tensor product restriction on the measurements performed by the
sender; without this restriction the trade-off is given by the regularization
of this function. Of particular interest is a quantity we call ``distillable
common randomness'' of a state: the maximum overhead of the common randomness
over the one-way classical communication if the latter is unbounded. It is an
operational measure of (total) correlation in a quantum state. For
classical-quantum correlations it is given by the Holevo mutual information of
its associated ensemble, for pure states it is the entropy of entanglement. In
general, it is given by an optimization problem over measurements and
regularization; for the case of separable states we show that this can be
single-letterized.Comment: 22 pages, LaTe
Distillation of secret key and entanglement from quantum states
We study and solve the problem of distilling secret key from quantum states
representing correlation between two parties (Alice and Bob) and an
eavesdropper (Eve) via one-way public discussion: we prove a coding theorem to
achieve the "wire-tapper" bound, the difference of the mutual information
Alice-Bob and that of Alice-Eve, for so-called cqq-correlations, via one-way
public communication.
This result yields information--theoretic formulas for the distillable secret
key, giving ``ultimate'' key rate bounds if Eve is assumed to possess a
purification of Alice and Bob's joint state.
Specialising our protocol somewhat and making it coherent leads us to a
protocol of entanglement distillation via one-way LOCC (local operations and
classical communication) which is asymptotically optimal: in fact we prove the
so-called "hashing inequality" which says that the coherent information (i.e.,
the negative conditional von Neumann entropy) is an achievable EPR rate.
This result is well--known to imply a whole set of distillation and capacity
formulas which we briefly review.Comment: 17 pages LaTeX, 1 drawing (eps
Exact Cost of Redistributing Multipartite Quantum States
How correlated are two quantum systems from the perspective of a third? We answer this by providing an optimal âquantum state redistributionâ protocol for multipartite product sources. Specifically, given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, we identify the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob. The communication cost gives the first known operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived
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