



01030nas a2200121   4500008004100000245008400041210006900125260001500194520062400209100001800833700002000851856003700871       2012                        eng d00aNon-Additivity of the Entanglement of Purification (Beyond Reasonable  Doubt)
0 aNonAdditivity of the Entanglement of Purification Beyond Reasona  c2012/06/063 a  We demonstrate the convexity of the difference between the regularized
entanglement of purification and the entropy, as a function of the state. This
is proved by means of a new asymptotic protocol to prepare a state from
pre-shared entanglement and by local operations only. We go on to employ this
convexity property in an investigation of the additivity of the (single-copy)
entanglement of purification: using numerical results for two-qubit Werner
states we find strong evidence that the entanglement of purification is
different from its regularization, hence that entanglement of purification is
not additive.
1 aChen, Jianxin1 aWinter, Andreas  uhttp://arxiv.org/abs/1206.1307v102114nas a2200169   4500008004100000245009200041210006900133260001300202490000700215520160400222100001801826700001401844700001701858700001801875700001401893856003701907       2011                        eng d00aNo-go Theorem for One-way Quantum Computing on Naturally Occurring  Two-level Systems
0 aNogo Theorem for Oneway Quantum Computing on Naturally Occurring  c2011/5/90 v833 a  One-way quantum computing achieves the full power of quantum computation by
performing single particle measurements on some many-body entangled state,
known as the resource state. As single particle measurements are relatively
easy to implement, the preparation of the resource state becomes a crucial
task. An appealing approach is simply to cool a strongly correlated quantum
many-body system to its ground state. In addition to requiring the ground state
of the system to be universal for one-way quantum computing, we also want the
Hamiltonian to have non-degenerate ground state protected by a fixed energy
gap, to involve only two-body interactions, and to be frustration-free so that
measurements in the course of the computation leave the remaining particles in
the ground space. Recently, significant efforts have been made to the search of
resource states that appear naturally as ground states in spin lattice systems.
The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet,
it remains an open question whether there could be such a natural resource
state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to
this question by proving that it is impossible for a genuinely entangled qubit
states to be a non-degenerate ground state of any two-body frustration-free
Hamiltonian. What is more, we prove that every spin-1/2 frustration-free
Hamiltonian with two-body interaction always has a ground state that is a
product of single- or two-qubit states, a stronger result that is interesting
independent of the context of one-way quantum computing.
1 aChen, Jianxin1 aChen, Xie1 aDuan, Runyao1 aJi, Zhengfeng1 aZeng, Bei  uhttp://arxiv.org/abs/1004.3787v1