Fine-grained EPR-steering inequalities

We derive a new steering inequality based on a fine-grained uncertainty relation to capture EPR-steering for bipartite systems. Our steering inequality improves over previously known ones since it can experimentally detect all steerable two-qubit Werner state with only two measurement settings on each side. According to our inequality, pure entangle states are maximally steerable. Moreover, by slightly changing the setting, we can express the amount of violation of our inequality as a function of their violation of the CHSH inequality. Finally, we prove that the amount of violation of our steering inequality is, up to a constant factor, a lower bound on the key rate of a one-sided device independent quantum key distribution protocol secure against individual attacks. To show this result, we first derive a monogamy relation for our steering inequality.Comment: 5 pages, Accepted for publication as a Rapid Communication in Physical Review

Quantum attacks against iterated block ciphers

We study the amplification of security against quantum attacks provided by iteration of block ciphers. In the classical case, the Meet-in-the-middle attack is a generic attack against those constructions. This attack reduces the time required to break double iterations to only twice the time it takes to attack a single block cipher, given that the attacker has access to a large amount of memory. More abstractly, it shows that security by composition does not achieve exact multiplicative amplification. We present a quantized version of this attack based on an optimal quantum algorithm for the Element Distinctness problem. We then use the generalized adversary method to prove the optimality of the attack. An interesting corollary is that the time-space tradeoff for quantum attacks is very different from what classical attacks allow. This first result seems to indicate that composition resists better to quantum attacks than to classical ones because it prevents the quadratic speedup achieved by quantizing an exhaustive search. We investigate security amplification by composition further by examining the case of four iterations. We quantize a recent technique called the dissection attack using the framework of quantum walks. Surprisingly, this leads to better gains over classical attacks than for double iterations, which seems to indicate that when the number of iterations grows, the resistance against quantum attacks decreases.Comment: 14 page

A Simple Bargaining Mechanism That Elicits Truthful Reservation Prices

We describe a simple 2-stage mechanism that induces two bargainers to be truthful in reporting their reservation prices in a 1st stage. If these prices criss-cross, the referee reports that they overlap, and the bargainers proceed to make offers in a 2nd stage. The average of the 2nd-stage offers becomes the settlement if both offers fall into the overlap interval; if only one offer falls into this interval, it is the settlement, but is implemented with probability 1/2; if neither offer falls into the interval, there is no settlement. Thus, if the bargainers reach the 2nd stage, they know their reservation prices overlap even if they fail to reach a settlement, possibly motivating them to try again.Bargaining; truth-telling mechanisms; probabilistic implementation

Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames

Multipartite nonlocality is of great fundamental interest and constitutes a useful resource for many quantum information protocols. However, demonstrating it in practice, by violating a Bell inequality, can be difficult. In particular, standard experimental setups require the alignment of distant parties' reference frames, which can be challenging or impossible in practice. In this work we study the violation of certain Bell inequalities, namely the Mermin, Mermin-Klyshko and Svetlichny inequalities, without shared reference frames, when parties share a Greenberger-Horne-Zeilinger (GHZ) state. Furthermore, we analyse how these violations demonstrate genuine multipartite features of entanglement and nonlocality. For 3, 4 and 5 parties, we show that it is possible to violate these inequalities with high probability, when the parties choose their measurements from the three Pauli operators, defined only with respect to their local frames. Moreover, the probability of violation, and the amount of violation, are increased when each party chooses their measurements from the four operators describing the vertices of a tetrahedron. We also consider how many randomly chosen measurement directions are needed to violate the Bell inequalities with high probability. We see that the obtained levels of violation are sufficient to also demonstrate genuine multipartite entanglement and nonseparability. Finally, we show analytically that choosing from two measurement settings per party is sufficient to demonstrate the maximum degree of genuine multipartite entanglement and nonseparability with certainty when the parties' reference frames are aligned in one direction so that they differ only in rotations around one axis

A Simple Bargaining Mechanism That Elicits Truthful Reservation Prices

We describe a simple 2-stage mechanism that induces two bargainers to be truthful in reporting their reservation prices in a 1st stage. If these prices criss-cross, the referee reports that they overlap, and the bargainers proceed to make offers in a 2nd stage. The average of the 2nd-stage offers becomes the settlement if both offers fall into the overlap interval; if only one offer falls into this interval, it is the settlement, but is implemented with probability 1/2; if neither offer falls into the interval, there is no settlement. Thus, if the bargainers reach the 2nd stage, they know their reservation prices overlap even if they fail to reach a settlement, possibly motivating them to try again.Bargaining; truth-telling mechanisms; probabilistic implementation; incomplete information.

Experimental detection of steerability in Bell local states with two measurement settings

Steering, a quantum property stronger than entanglement but weaker than non-locality in the quantum correlation hierarchy, is a key resource for one-sided device-independent quantum key distribution applications, in which only one of the communicating parties is trusted. A fine-grained steering inequality was introduced in [PRA 90 050305(R) (2014)], enabling for the first time the detection of steering in all steerable two-qubit Werner states using only two measurement settings. Here we numerically and experimentally investigate this inequality for generalized Werner states and successfully detect steerability in a wide range of two-photon polarization-entangled Bell local states generated by a parametric down-conversion source.Comment: 9 pages, 7 figures (including Appendix

The Potentate of P.I.O. : [Judith Schwartz]

Rockefeller University Research Profiles are a series of scientific profiles that were published quarterly, from 1980-1990, by the Rockefeller University. Each issue features the research and achievements of an individual Rockefeller University scientist.https://digitalcommons.rockefeller.edu/research_profiles/1037/thumbnail.jp