142 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
Approximate unitary -designs by short random quantum circuits using nearest-neighbor and long-range gates
We prove that -depth local random quantum circuits
with two qudit nearest-neighbor gates on a -dimensional lattice with n
qudits are approximate -designs in various measures. These include the
"monomial" measure, meaning that the monomials of a random circuit from this
family have expectation close to the value that would result from the Haar
measure. Previously, the best bound was due to
Brandao-Harrow-Horodecki (BHH) for . We also improve the "scrambling" and
"decoupling" bounds for spatially local random circuits due to Brown and Fawzi.
One consequence of our result is that assuming the polynomial hierarchy (PH)
is infinite and that certain counting problems are -hard on average,
sampling within total variation distance from these circuits is hard for
classical computers. Previously, exact sampling from the outputs of even
constant-depth quantum circuits was known to be hard for classical computers
under the assumption that PH is infinite. However, to show the hardness of
approximate sampling using this strategy requires that the quantum circuits
have a property called "anti-concentration", meaning roughly that the output
has near-maximal entropy. Unitary 2-designs have the desired anti-concentration
property. Thus our result improves the required depth for this level of
anti-concentration from linear depth to a sub-linear value, depending on the
geometry of the interactions. This is relevant to a recent proposal by the
Google Quantum AI group to perform such a sampling task with 49 qubits on a
two-dimensional lattice and confirms their conjecture that depth
suffices for anti-concentration. We also prove that anti-concentration is
possible in depth O(log(n) loglog(n)) using a different model
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
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