708 research outputs found
Qubit-qudit states with positive partial transpose
We show that the length of a qubit-qutrit separable state is equal to the
max(r,s), where r is the rank of the state and s is the rank of its partial
transpose. We refer to the ordered pair (r,s) as the birank of this state. We
also construct examples of qubit-qutrit separable states of any feasible birank
(r,s). We determine the closure of the set of normalized two-qutrit entangled
states of rank four having positive partial transpose (PPT). The boundary of
this set consists of all separable states of length at most four. We prove that
the length of any qubit-qudit separable state of birank (d+1,d+1) is d+1. We
also show that all qubit-qudit PPT entangled states of birank (d+1,d+1) can be
built in a simple way from edge states. If V is a subspace of dimension k<d in
the tensor product of C^2 and C^d such that V contains no product vectors, we
show that the set of all product vectors in the orthogonal complement of V is a
vector bundle of rank d-k over the projective line. Finally, we explicitly
construct examples of qubit-qudit PPT states (both separable and entangled) of
any feasible birank.Comment: 13 pages, 2 table
QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB
A program package for MATLAB is introduced that helps calculations in quantum
information science and quantum optics. It has commands for the following
operations: (i) Reordering the qudits of a quantum register, computing the
reduced state of a quantum register. (ii) Defining important quantum states
easily. (iii) Formatted input and output for quantum states and operators. (iv)
Constructing operators acting on given qudits of a quantum register and
constructing spin chain Hamiltonians. (v) Partial transposition, matrix
realignment and other operations related to the detection of quantum
entanglement. (vi) Generating random state vectors, random density matrices and
random unitaries.Comment: 22 pages, no figures; small changes, published versio
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