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Physica Scripta

The illusionist game and hidden correlations

G. Brida, Ivo Pietro Degiovanni, Marco Genovese, Alice Meda, Stefano Olivares, Matteo G. A. Paris

Published Mar 1, 2013• 4 citations
Publisher

Abstract

We suggest and demonstrate a new protocol based on correlated beams of light: the ‘optical illusionist game’. An ‘illusionist’ at first shows that if two uncorrelated light beams excited in the same Gaussian state are mixed in a beam splitter, then no correlations arise between them, as it was not present. On the other hand, when correlations with an ancillary state are exploited, the presence of the beam splitter can be unveiled.

DOI
10.1088/0031-8949/2013/t153/014006

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We suggest and demonstrate a new protocol based on correlated beams of light: the ‘optical illusionist game’. An ‘illusionist’ at first shows that if two uncorrelated light beams excited in the same Gaussian state are mixed in a beam splitter, then no correlations arise between them, as it was not present. On the other hand, when correlations with an ancillary state are exploited, the presence of the beam splitter can be unveiled.
Optical correlations represent a resource for the development of technologies with very promising opportunities for future widespread applications.1–14 Here we will show, both theoretically and experimentally, the optical illusionist game, an innovative protocol that exploit correlations between thermal beams of light.15 In the game, an illusionist demonstrates that if two uncorrelated light beams excited in the same state are mixed in a beam splitter (BS), then no correlations arise between them. On the other hand, the presence of the BS can be identified by the illusionist when the public is asked to insert the BS behind the illusionist’s back. Here we unveil the trick and the physics that explain these counterintuitive correlations. 1
In general, a pair of uncorrelated Gaussian states mixed in a beam splitter (BS) produces a correlated state at the output. However, when the inputs are identical Gaussian states the output state is equal to the input, and no correlations appear, as the interference had not taken place. On the other hand, since physical phenomena do have observable effects, and the BS is there, a question arises on how to reveal the interference between the two beams. We prove theoretically and demonstrate experimentally that this is possible if at least one of the two beams is prepared in a discordant, i.e., Gaussian correlated, state with a third beam. We also apply the same technique to reveal the erasure of polarization information. Our experiment involves thermal states and the results show that Gaussian discordant states, even when they show a positive Glauber P-function, may be useful to achieve specific tasks.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
Abstract In this paper, we investigate the creation of quantum correlations such as entanglement, the Gaussian quantum discord and quantum steering in a quantum system under consideration via the linear beam splitter with squeezed thermal and a single-mode Gaussian states at the inputs. This quantum system generates bright entangled output two-mode light. Specifically, the quantum entanglement can be enhanced through increasing the purity of the Gaussian state and the squeezing parameter at the input states. The quantum correlations reveal similar characteristics for each case. That means when we increase the non-classicality, purity and squeezing parameter, the quantum correlations show enhanced profile. On the other hand, upon increasing the mean thermal photon number at the input, the quantum correlations indicate inverse relation.
We propose a new experiment employing two independent sources of spin correlated photon pairs. Two photons from different unpolarized sources each pass through a polarizer to a detector. Although their trajectories never mix or cross, they exhibit fourth-order-interference-like correlations when the other two photons interfere on a beam splitter even when the latter two do not pass any polarizers at all. A wave packet calculation shows that the experiment permits a very discriminatory test of hidden variable theories.