Quantum Mutual Information Capacity for High-Dimensional Entangled States

Abstract

High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.

Einstein-Podolsky-Rosen Paradox in Twin Images

“…The conditional probability distributions calculated using 35000 images are shown in Fig.2. The correlation profiles agree with the theoretical expectations (2) and (3) with σ p >> σ φ .…”

“…Though the original intention of EPR was to show that quantum mechanics is not complete, the standard present view is that entangled particles do experience nonlocal correlations 9,10 . It can be shown that the spatial extent of these correlations corresponds to the size of a spatial unit of information, or mode, offering the possibility of detecting high dimensional entanglement in an image with a sufficient number of resolution cells 2,4 . However, in most experiments the use of single photon detectors and coincidence counting leads to the detection of a very few part of selected photons, generating a sampling loophole in fundamental demonstrations.…”

“…Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement 1,2 , and a test of the Einstein-Podolsky-Rosen (EPR) paradox 3 in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatio-temporal behavior 4 .…”

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

“…In addition, we note that the position and momentum referred to in this paper are not field quadratures, but actual positions and momenta of downconverted photons as seen in Ref. [5]. Our inequality (2) provides both a simpler and more powerful method to successfully witness EPR steering.…”

“…Violating EPR steering for continuous variables (CV) is understandably challenging because CV systems are infinitedimensional. As interest in EPR steering increases, including interest regarding its fundamental aspects [3][4][5][6][7][8][9], as well as its use in quantum information applications such as secure quantum key distribution [10], witnesses of CV EPR steering become increasingly important.…”