Practically state-independent test of contextuality with 9 observables

We propose a test of quantum contextuality for a single three-level system that uses nine projective measurements. It has a form of an inequality that has to be satisfied by any non-contextual theory and which is violated by any quantum state, except for the maximally mixed one. Due to the fact that there is only a single state that does not exhibit contextuality, it is natural to ask what the difference between state-independent tests and the one proposed here is.Comment: 3 pages, 1 figur

Complementarity Relations Between Quantum Steering Criteria

Recently, a connection between quantum coherence and quantum steering was established and criteria for quantum steering or in other words, nonlocal advantage of quantum coherence (NAQC) were derived for two-qubit states. Here, we derive a set of complementarity relations between the steering or NAQC inequalities achieved by various criteria. We also extend the idea in the multi-partite scenario, specifically, in the three-qubit scenario, which can easily be generalized to the multi-partite scenario.Comment: 6 pages, 3 figure

Entropic tests of multipartite nonlocality and state-independent contextuality

We introduce a multipartite extension of an information-theoretic distance first introduced in [Nature 341, 119 (1989)]. We use this new distance to derive entropic tests of multipartite nonlocality for three and for an arbitrary even number of qubits as well as a test of state-independent contextuality. In addition, we re-derive the tripartite Mermin inequality and a state-independent non-contextuality inequality by Cabello [Phys. Rev. Lett. 101, 210401 (2008)]. This suggests that the information-theoretic distance approach to multipartite nonlocality and state-independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions.Comment: 5 pages, 3 figures, extended version of arXiv:1409.7290 with more general result

Dimensionality induced entanglement in macroscopic dimer systems

We investigate entanglement properties of mixtures of short-range spin-s dimer coverings in lattices of arbitrary topology and dimension. We show that in one spacial dimension nearest neighbour entanglement exists for any spin $s$. Surprisingly, in higher spatial dimensions there is a threshold value of spin $s$ below which the nearest neighbour entanglement disappears. The traditional "classical" limit of large spin value corresponds to the highest nearest neighbour entanglement that we quantify using the negativity.Comment: 4 pages, 2 figure

Optimal Asymmetric Quantum Cloning

While the no-cloning theorem, which forbids the perfect copying of quantum states, is well-known as one of the defining features of quantum mechanics, the question of how well the theory allows a state to be cloned is yet to be completely solved. In this paper, rigorous solutions to the problem of M to N asymmetric cloning of qudits are obtained in a number of interesting cases. The central result is the solution to the 1 to N universal asymmetric qudit cloning problem for which the exact trade-off in the fidelities of the clones for every N and d is derived. Analogous results are proven for qubits when M=N-1. We also consider state-dependent 1 to N qubit cloning, providing a general parametrization in terms of a Heisenberg star Hamiltonian. In all instances, we determine the feasibility of implementing the cloning economically, i.e., without an ancilla, and determine the dimension of the ancilla when an economic implementation is not possible.Comment: 12 page