Trade-offs in multi-party Bell inequality violations in qubit networks

Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the sole assumption of no signalling. We first investigate the trade-offs in Bell violations arising from the uncertainty relation for complementary binary observables, and exhibit several network configurations in which a tight trade-off arises in this fashion. We then derive a tight trade-off relation which cannot be obtained from the uncertainty relation showing that it does not capture monogamy entirely. The results are extended to Bell inequalities involving different number of parties and find applications in device-independent secret sharing and device-independent randomness extraction. Although two multipartite Bell inequalities may be violated simultaneously, we show that genuine multi-party non-locality, as evidenced by a generalised Svetlichny inequality, does exhibit monogamy property. Finally, using the relations derived we reveal the existence of flat regions in the set of quantum correlations.Comment: 15 pages, 5 figure

Finite Device-Independent Extraction of a Block Min-Entropy Source against Quantum Adversaries

The extraction of randomness from weakly random seeds is a problem of central importance with multiple applications. In the device-independent setting, this problem of quantum randomness amplification has been mainly restricted to specific weak sources of Santha-Vazirani type, while extraction from the general min-entropy sources has required a large number of separated devices which is impractical. In this paper, we present a device-independent protocol for amplification of a single min-entropy source (consisting of two blocks of sufficiently high min-entropy) using a device consisting of two spatially separated components and show a proof of its security against general quantum adversaries.Comment: 17 page

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

Single trusted qubit is necessary and sufficient for quantum realisation of extremal no-signaling correlations

Quantum statistics can be considered from the perspective of postquantum no-signaling theories in which either none or only a certain number of quantum systems are trusted. In these scenarios, the role of states is played by the so-called no-signaling boxes or no-signaling assemblages respectively. It has been shown so far that in the usual Bell non-locality scenario with a single measurement run, quantum statistics can never reproduce an extremal non-local point within the set of no-signaling boxes. We provide here a general no-go rule showing that the latter stays true even if arbitrary sequential measurements are allowed. On the other hand, we prove a positive result showing that already a single trusted qubit is enough for quantum theory to produce a self-testable extremal point within the corresponding set of no-signaling assemblages. This result opens up the possibility for security proofs of cryptographic protocols against general no-signaling adversaries.Comment: 14 page

Quantum bounds on multiplayer linear games and device-independent witness of genuine tripartite entanglement

Here we study multiplayer linear games, a natural generalization of XOR games to multiple outcomes. We generalize a recently proposed efficiently computable bound, in terms of the norm of a game matrix, on the quantum value of 2-player games to linear games with $n$ players. As an example, we bound the quantum value of a generalization of the well-known CHSH game to $n$ players and $d$ outcomes. We also apply the bound to show in a simple manner that any nontrivial functional box, that could lead to trivialization of communication complexity in a multiparty scenario, cannot be realized in quantum mechanics. We then present a systematic method to derive device-independent witnesses of genuine tripartite entanglement.Comment: 7+8 page

The relation between nonlocality and contextuality for a biphoton

We investigate the set of qutrit states in terms of symmetric states of two qubits that violate the minimal contextual inequality, namely the Klyachko-Can-Binicoglu-Shumovsky (KCBS) inequality. The physical system that provides a natural framework for this problem is a biphoton which consists of two photons in the same spatio-temporal mode and whose effective polarization behaves as a three-level quantum system. The relationship between the KCBS contextual inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality is investigated. We find that every biphotonic state that is contextual with respect to KCBS is nonlocal as per the CHSH test when the two photons are apart, but the converse is not true.Comment: Close to the published versio