Optimal cloning for two pairs of orthogonal states

We study the optimal cloning transformation for two pairs of orthogonal states of two-dimensional quantum systems, and derive the corresponding optimal fidelities.Comment: 4 pages, 3 figure

Multipartite entanglement in quantum algorithms

We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement

Multipartite entanglement in quantum algorithms

We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement

Experimental generation of pseudo bound entanglement

We use Nuclear Magnetic Resonance (NMR) to experimentally generate a bound entangled (more precisely: pseudo bound entangled) state, i.e. a quantum state which is non-distillable but nevertheless entangled. Our quantum system consists of three qubits. We characterize the produced state via state tomography to show that the created state has a positive partial transposition with respect to any bipartite splitting, and we use a witness operator to prove its entanglement.Comment: 5 page

Optimal eavesdropping in cryptography with three-dimensional quantum states

We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.Comment: 4 pages, 2 figure

Quantum Hypergraph States

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.Comment: 9+5 pages, 5 figures, 1 table, published versio

Quantum Cloning in dd dimensions

The quantum state space $\cal S$ over a $d$-dimensional Hilbert space is represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset {\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then associated with the affine transformations of ${\bf{R}}^D,$ and $N\mapsto M$ {\it cloners} induce polynomial mappings. In this geometrical setting it is shown that an optimal cloner can be chosen covariant and induces a map between reduced density matrices given by a simple contraction of the associated $D$-dimensional Bloch vectors.Comment: 8 pages LaTeX, no figure

Quantum cloning machines for equatorial qubits

Quantum cloning machines for equatorial qubits are studied. For the case of 1 to 2 phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal 1 to M phase-covariant quantum cloning transformations are given.Comment: Revtex, 9 page

Generalized self-testing and the security of the 6-state protocol

Self-tested quantum information processing provides a means for doing useful information processing with untrusted quantum apparatus. Previous work was limited to performing computations and protocols in real Hilbert spaces, which is not a serious obstacle if one is only interested in final measurement statistics being correct (for example, getting the correct factors of a large number after running Shor's factoring algorithm). This limitation was shown by McKague et al. to be fundamental, since there is no way to experimentally distinguish any quantum experiment from a special simulation using states and operators with only real coefficients. In this paper, we show that one can still do a meaningful self-test of quantum apparatus with complex amplitudes. In particular, we define a family of simulations of quantum experiments, based on complex conjugation, with two interesting properties. First, we are able to define a self-test which may be passed only by states and operators that are equivalent to simulations within the family. This extends work of Mayers and Yao and Magniez et al. in self-testing of quantum apparatus, and includes a complex measurement. Second, any of the simulations in the family may be used to implement a secure 6-state QKD protocol, which was previously not known to be implementable in a self-tested framework.Comment: To appear in proceedings of TQC 201

On the generalization of quantum state comparison

We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities. We show that the optimal coherent measurement is always superior to the optimal incoherent measurement. Second, we develop a strategy for the comparison of two states from a set of N pure states, and find an optimal solution for some parameter range when N=3. In both cases we use the reduction method for the corresponding problem of mixed state discrimination, as introduced by Raynal et al., which reduces the problem to the discrimination of two pure states only for N=2. Finally, we provide a necessary and sufficient condition for unambiguous comparison of mixed states to be possible.Comment: 8 pages, 4 figures, Proposition 1 corrected, appendix adde