4,914 research outputs found
Stabilizer States as a Basis for Density Matrices
We show that the space of density matrices for n-qubit states, considered as
a (2^n)^2 dimensional real vector space, has a basis consisting of density
matrices of stabilizer states. We describe an application of this result to
automated verification of quantum protocols
Undetermined states: how to find them and their applications
We investigate the undetermined sets consisting of two-level, multi-partite
pure quantum states, whose reduced density matrices give absolutely no
information of their original states. Two approached of finding these quantum
states are proposed. One is to establish the relation between codewords of the
stabilizer quantum error correction codes (SQECCs) and the undetermined states.
The other is to study the local complementation rules of the graph states. As
an application, the undetermined states can be exploited in the quantum secret
sharing scheme. The security is guaranteed by their undetermineness.Comment: 6 pages, no figur
Symmetric mixed states of qubits: local unitary stabilizers and entanglement classes
We classify, up to local unitary equivalence, local unitary stabilizer Lie
algebras for symmetric mixed states into six classes. These include the
stabilizer types of the Werner states, the GHZ state and its generalizations,
and Dicke states. For all but the zero algebra, we classify entanglement types
(local unitary equivalence classes) of symmetric mixed states that have those
stabilizers. We make use of the identification of symmetric density matrices
with polynomials in three variables with real coefficients and apply the
representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for
published versio
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