112 research outputs found
Coherent Communication of Classical Messages
We define "coherent communication" in terms of a simple primitive, show it is
equivalent to the ability to send a classical message with a unitary or
isometric operation, and use it to relate other resources in quantum
information theory. Using coherent communication, we are able to generalize
super-dense coding to prepare arbitrary quantum states instead of only
classical messages. We also derive single-letter formulae for the classical and
quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed
amount of entanglement per use.Comment: 5 pages, revtex, v2: updated references, v3: changed title, fixed
error in eq (10
How many copies are needed for state discrimination?
Given a collection of states (rho_1, ..., rho_N) with pairwise fidelities
F(rho_i, rho_j) <= F < 1, we show the existence of a POVM that, given
rho_i^{otimes n}, will identify i with probability >= 1-epsilon, as long as
n>=2(log N/eps)/log (1/F). This improves on previous results which were either
dimension-dependent or required that i be drawn from a known distribution.Comment: 1 page, submitted to QCMC'06, answer is O(log # of states
Extremal eigenvalues of local Hamiltonians
We apply classical algorithms for approximately solving constraint
satisfaction problems to find bounds on extremal eigenvalues of local
Hamiltonians. We consider spin Hamiltonians for which we have an upper bound on
the number of terms in which each spin participates, and find extensive bounds
for the operator norm and ground-state energy of such Hamiltonians under this
constraint. In each case the bound is achieved by a product state which can be
found efficiently using a classical algorithm.Comment: 5 pages; v4: uses standard journal styl
Bidirectional coherent classical communication
A unitary interaction coupling two parties enables quantum communication in
both the forward and backward directions.
Each communication capacity can be thought of as a tradeoff between the
achievable rates of specific types of forward and backward communication.
Our first result shows that for any bipartite unitary gate, coherent
classical communication is no more difficult than classical communication --
they have the same achievable rate regions. Previously this result was known
only for the unidirectional capacities (i.e., the boundaries of the tradeoff).
We then relate the tradeoff curve for two-way coherent communication to the
tradeoff for two-way quantum communication and the tradeoff for coherent
communiation in one direction and quantum communication in the other.Comment: 11 pages, v2 extensive modification and rewriting of the main proof,
v3 published version with only a few more change
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