Ravishankar Ramanathan

Entropic test of quantum contextuality.

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves [Phys. Rev. Lett. 61, 662 (1988)], that must be satisfied by all noncontextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.

Generalized monogamy of contextual inequalities from the no-disturbance principle.

In this Letter, we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

Realistic noise-tolerant randomness amplification using finite number of devices.

Randomness is a fundamental concept, with implications from security of modern data systems, to fundamental laws of nature and even the philosophy of science. Randomness is called certified if it describes events that cannot be pre-determined by an external adversary. It is known that weak certified randomness can be amplified to nearly ideal randomness using quantum-mechanical systems. However, so far, it was unclear whether randomness amplification is a realistic task, as the existing proposals either do not tolerate noise or require an unbounded number of different devices. Here we provide an error-tolerant protocol using a finite number of devices for amplifying arbitrary weak randomness into nearly perfect random bits, which are secure against a no-signalling adversary. The correctness of the protocol is assessed by violating a Bell inequality, with the degree of violation determining the noise tolerance threshold. An experimental realization of the protocol is within reach of current technology.Fernando G.S.L. Brandão,1 Ravishankar Ramanathan,2, 3 Andrzej Grudka,4 Karol Horodecki,2, 5 Michał Horodecki,2, 3 and Paweł Horodecki2, 6 1Department of Computer Science, University College London 2National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland 3Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland 4Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland 5Institute of Informatics, University of Gdańsk, 80-952 Gdańsk, Poland 6Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdańsk, Poland (Dated: October 18, 2013)

Free randomness amplification using bipartite chain correlations

A direct analysis of the task of randomness amplification from Santha-Vazirani sources using the violation of the chained Bell inequality is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. This analysis is used to find the exact threshold value of the initial randomness parameter from which perfect randomness can be extracted in the asymptotic limit of a large number of measurement settings. As a byproduct, we provide a tool for the analysis of randomness amplification protocols, namely a general characterization of the probability distributions of bits generated by Santha-Vazirani sources, which are shown to be mixtures of specific permutations of Bernoulli distributions with a parameter defined by the source.

Correlation complementarity yields bell monogamy relations.

We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.

Local Realism of Macroscopic Correlations

We identify conditions under which correlations resulting from quantum measurements performed on macroscopic systems (systems composed of a number of particles of the order of the Avogadro number) can be described by local realism. We argue that the emergence of local realism at the macroscopic level is caused by an interplay between the monogamous nature of quantum correlations and the fact that macroscopic measurements do not reveal properties of individual particles.

Randomness amplification against no-signaling adversaries using two devices

Ravishankar Ramanathan,1, 2 Fernando G.S.L. Brandão,3, 4 Karol Horodecki,1, 5 Michał Horodecki,1, 2 Paweł Horodecki,1, 6 and Hanna Wojewódka1, 2, 7 National Quantum Information Center of Gdańsk, 81-824 Sopot, Poland Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland Quantum Architectures and Computations Group, Microsoft Research, Redmond, WA (USA) Department of Computer Science, University College London Institute of Informatics, University of Gdańsk, 80-952 Gdańsk, Poland Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, 80-233 Gdańsk, Poland Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland (Dated: April 24, 2015)

No Quantum Realization of Extremal No-Signaling Boxes.

The study of quantum correlations is important for fundamental reasons as well as for quantum communication and information processing tasks. On the one hand, it is of tremendous interest to derive the correlations produced by measurements on separated composite quantum systems from within the set of all correlations obeying the no-signaling principle of relativity, by means of information-theoretic principles. On the other hand, an important ongoing research program concerns the formulation of device-independent cryptographic protocols based on quantum nonlocal correlations for the generation of secure keys, and the amplification and expansion of random bits against general no-signaling adversaries. In both these research programs, a fundamental question arises: Can any measurements on quantum states realize the correlations present in pure extremal no-signaling boxes? Here, we answer this question in full generality showing that no nontrivial (not local realistic) extremal boxes of general no-signaling theories can be realized in quantum theory. We then explore some important consequences of this fact.

Necessary and sufficient condition for state-independent contextual measurement scenarios.

The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension d and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph χf(G) and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.

Particle addition and subtraction channels and the behavior of composite particles

Pawe l Kurzyński, 2 Ravishankar Ramanathan, Akihito Soeda, Tan Kok Chuan, and Dagomir Kaszlikowski ∗ Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland Department of Physics, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore (Dated: April 28, 2013)Composite particles made of elementary fermions can exhibit a wide range of behavior ranging from fermionic to bosonic depending on the quantum state of the fermions and the experimental situation considered. This behavior is captured by the fundamental operations of single-particle addition and subtraction and two-particle interference. We analyze the quantum channels that implement the physical operations of addition and subtraction of indistinguishable particles. In particular, we construct optimal Kraus operators to implement these probabilistic operations for systems of a finite number of particles. We then use these to measure the quality of bosonic and fermionic behavior in terms of single-particle addition and subtraction and two-particle interference. For the specific case of composite particles made of two distinguishable fermions, we find a transition from fermionic to bosonic behavior as a function of the entanglement between the two constituents. We also apply these considerations to composite particles of two distinguishable bosons and identify the relation between entanglement and bosonic behavior for these systems.