Arijit Dutta

Geometric Bell-like inequalities for steering

Many of the standard Bell inequalities (e.g., CHSH) are not effective for detection of quantum correlations which allow for steering, because for a wide range of such correlations they are not violated. We present Bell-like inequalities which have lower bounds for non-steering correlations than for local causal models. The inequalities involve all possible measurement settings at each side. We arrive at interesting and elegant conditions for steerability of arbitrary two-qubit states.

Entanglement criteria for noise resistance of two-qudit states

Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by d × d Hilbert space. Our analysis uses a geometric approach based on the fact that if a scalar product of a vector ~s with a vector ~e is less than the square of the norm of ~e, then ~s 6= ~e. We use such concepts for correlation tensors of separable and entangled states. As a general form correlation tensors for pairs of qudits, for d > 2, is very difficult to obtain, because one does not have a Bloch sphere for pure one qudit states, we use a simplified approach. The criterion reads: if the largest Schmidt eigenvalue of a correlation tensor is smaller than the square of its norm, then the state is entangled. this criterion is applied in the case of various types of noise admixtures to the initial (pure) state. These include white noise, colored noise, local depolarizing noise and amplitude damping noise. A broad set of numerical and analytical results is presented. As the other simple criterion for entanglement is violation of Bell’s inequalities, we also find critical noise parameters to violate specific family of Bell inequalities (CGLMP), for maximally entangled states. We give analytical forms of our results for d approaching infinity.

Detection-efficiency loophole and the Pusey-Barrett-Rudolph theorem

Detection efficiency loophole poses a significant problem for experimental tests of Bell inequalities. Recently discovered Pusey-Barrett-Rudolph (PBR) theorem suffers from the same vulnerability. In this paper we calculate the critical detection efficiency, below which the PBR argument for the ontic nature of quantum state is inconclusive. This is done for the maximally

Geometric chained inequalities for higher-dimensional systems

\psi

Clearer visibility of the Hong-Ou-Mandel effect with a correlation function based on rates rather than intensities

-epistemic models. We use two different definitions of this property. The optimal number of parties, for which the critical detection efficiency is the lowest is given. We also approach the problem from the opposite direction. We provide a function which enables us to specify which epistemic models are ruled out by the results of an experiment with a given detection efficiency.

Geometric extension of Clauser–Horne inequality to more qubits

For systems of an arbitrary dimension, a theory of geometric chained Bell inequalities is presented. The approach is based on chained inequalities derived by Pykacz and Santos. For maximally entangled states the inequalities lead to a complete

Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies

0=1

Multisetting Bell inequalities for N spin-1 systems avoiding the Kochen-Specker contradiction

contradiction with quantum predictions. Local realism suggests that the probability for the two observes to have identical results is

Optimal Usage of Quantum Random Access Memory in Quantum Machine Learning

1

Publisher's Note: Geometric Bell-like inequalities for steering [Phys. Rev. A91, 032107 (2015)]

(that is a perfect correlation is predicted), whereas quantum formalism gives an opposite prediction: the local results always differ. This is so for any dimension. We also show that with the inequalities, one can have a version of Bells theorem which involves only correlations arbitrarily close to perfect ones.