ar X iv : q ua nt - p h / 05 06 24 1 v 1 2 8 Ju n 20 05 Classification of n - qubit states with minimum orbit dimension

ua nt - p h / 05 06 24 1 v 2 1 8 O ct 2 00 5 Classification of n - qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...

ua nt - p h / 05 06 24 1 v 3 22 F eb 2 00 6 Classification of n - qubit states with minimum orbit dimension

The group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n+ 1)/2 for n odd, where n is the number of qubits. In this pap...

ar X iv : q ua nt - p h / 05 06 09 5 v 1 1 3 Ju n 20 05 Schmidt states and positivity of linear maps

Using pure entangled Schmidt states, we show that m-positivity of a map is bounded by the ranks of its negative Kraus matrices. We also give an algebraic condition for a map to be m-positive. We interpret these results in the context of positive maps as entanglement witnesses, and find that only 1-positive maps are needed for testing entanglement.

ar X iv : q ua nt - p h / 05 06 01 5 v 1 2 Ju n 20 05 Reply To “ Comment on ‘ Quantum Convolutional Error - Correcting Codes ’ ”

Theorem 3. Let C1 be a classical (block or convolutional) code of rate r1 and distance d1 and let C2 be the [n2 = d2, 1, d2] majority vote classical code of rate r2, namely, the one that maps |t〉 to ⊗n2 j=1 |t〉. We construct a quantum code C by first encoding a quantum state by C1, then by applying a Hadamard transform to every resultant qubit, and finally by encoding each of the Hadamard trans...

ar X iv : q ua nt - p h / 02 06 11 6 v 1 1 8 Ju n 20 02 Five Lectures On Dissipative Master Equations