TY - JOUR T1 - No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems JF - Physical Review A Y1 - 2011 A1 - Jianxin Chen A1 - Xie Chen A1 - Runyao Duan A1 - Zhengfeng Ji A1 - Bei Zeng AB - 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. VL - 83 UR - http://arxiv.org/abs/1004.3787v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.050301 ER - TY - JOUR T1 - Optimal Perfect Distinguishability between Unitaries and Quantum Operations Y1 - 2010 A1 - Cheng Lu A1 - Jianxin Chen A1 - Runyao Duan AB - We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations. UR - http://arxiv.org/abs/1010.2298v1 ER - TY - JOUR T1 - Existence of Universal Entangler JF - Journal of Mathematical Physics Y1 - 2008 A1 - Jianxin Chen A1 - Runyao Duan A1 - Zhengfeng Ji A1 - Mingsheng Ying A1 - Jun Yu AB - A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open. VL - 49 U4 - 012103 UR - http://arxiv.org/abs/0704.1473v2 CP - 1 J1 - J. Math. Phys. U5 - 10.1063/1.2829895 ER -