209 research outputs found
qubit "mirror states" for optimal quantum communication
We introduce a new genuinely 2N qubit state, known as the "mirror state" with
interesting entanglement properties. The well known Bell and the cluster states
form a special case of these "mirror states", for N=1 and N=2 respectively. It
can be experimentally realized using and multiply controlled phase shift
operations. After establishing the general conditions for a state to be useful
for various communicational protocols involving quantum and classical
information, it is shown that the present state can optimally implement
algorithms for the quantum teleportation of an arbitrary N qubit state and
achieve quantum information splitting in all possible ways. With regard to
superdense coding, one can send 2N classical bits by sending only N qubits and
consuming N ebits of entanglement. Explicit comparison of the mirror state with
the rearranged N Bell pairs and the linear cluster states is considered for
these quantum protocols. We also show that mirror states are more robust than
the rearranged Bell pairs with respect to a certain class of collisional
decoherence.Comment: To be published in EPJ
Genuinely multipartite entangled states and orthogonal arrays
A pure quantum state of N subsystems with d levels each is called
k-multipartite maximally entangled state, written k-uniform, if all its
reductions to k qudits are maximally mixed. These states form a natural
generalization of N-qudits GHZ states which belong to the class 1-uniform
states. We establish a link between the combinatorial notion of orthogonal
arrays and k-uniform states and prove the existence of several new classes of
such states for N-qudit systems. In particular, known Hadamard matrices allow
us to explicitly construct 2-uniform states for an arbitrary number of N>5
qubits. We show that finding a different class of 2-uniform states would imply
the Hadamard conjecture, so the full classification of 2-uniform states seems
to be currently out of reach. Additionally, single vectors of another class of
2-uniform states are one-to-one related to maximal sets of mutually unbiased
bases. Furthermore, we establish links between existence of k-uniform states,
classical and quantum error correction codes and provide a novel graph
representation for such states.Comment: 24 pages, 7 figures. Comments are very welcome
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