8 research outputs found
Maximum stabilizer dimension for nonproduct states
Composite quantum states can be classified by how they behave under local
unitary transformations. Each quantum state has a stabilizer subgroup and a
corresponding Lie algebra, the structure of which is a local unitary invariant.
In this paper, we study the structure of the stabilizer subalgebra for n-qubit
pure states, and find its maximum dimension to be n-1 for nonproduct states of
three qubits and higher. The n-qubit Greenberger-Horne-Zeilinger state has a
stabilizer subalgebra that achieves the maximum possible dimension for pure
nonproduct states. The converse, however, is not true: we show examples of pure
4-qubit states that achieve the maximum nonproduct stabilizer dimension, but
have stabilizer subalgebra structures different from that of the n-qubit GHZ
state.Comment: 6 page
Minimum orbit dimension for local unitary action on n-qubit pure states
The group of local unitary transformations partitions the space of n-qubit
quantum states into orbits, each of which is a differentiable manifold of some
dimension. We prove that all orbits of the n-qubit quantum state space have
dimension greater than or equal to 3n/2 for n even and greater than or equal to
(3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since
n-qubit states composed of products of singlets achieve these lowest orbit
dimensions.Comment: 19 page
Distribution of G-concurrence of random pure states
Average entanglement of random pure states of an N x N composite system is
analyzed. We compute the average value of the determinant D of the reduced
state, which forms an entanglement monotone. Calculating higher moments of the
determinant we characterize the probability distribution P(D). Similar results
are obtained for the rescaled N-th root of the determinant, called
G-concurrence. We show that in the limit this quantity becomes
concentrated at a single point G=1/e. The position of the concentration point
changes if one consider an arbitrary N x K bipartite system, in the joint limit
, K/N fixed.Comment: RevTeX4, 11 pages, 4 Encapsuled PostScript figures - Introduced new
results, Section II and V have been significantly improved - To appear on PR
Universal observable detecting all two-qubit entanglement and determinant based separability tests
We construct a single observable measurement of which mean value on four
copies of an {\it unknown} two-qubit state is sufficient for unambiguous
decision whether the state is separable or entangled. In other words, there
exists a universal collective entanglement witness detecting all two-qubit
entanglement. The test is directly linked to a function which characterizes to
some extent the entanglement quantitatively. This function is an entanglement
monotone under so--called local pure operations and classical communication
(pLOCC) which preserve local dimensions. Moreover it provides tight upper and
lower bounds for negativity and concurrence. Elementary quantum computing
device estimating unknown two-qubit entanglement is designed.Comment: 5 pages, RevTeX, one figure replaced by another, tight bounds on
negativity and concurrence added, function proved to be a monotone under the
pure LOCC, list of authors put in alphabetical orde
Wehrl entropy, Lieb conjecture and entanglement monotones
We propose to quantify the entanglement of pure states of
bipartite quantum system by defining its Husimi distribution with respect to
coherent states. The Wehrl entropy is minimal if and only
if the pure state analyzed is separable. The excess of the Wehrl entropy is
shown to be equal to the subentropy of the mixed state obtained by partial
trace of the bipartite pure state. This quantity, as well as the generalized
(R{\'e}nyi) subentropies, are proved to be Schur--convex, so they are
entanglement monotones and may be used as alternative measures of entanglement