We investigate how the polarization correlations of entangled photons described by wave packets are modified when measured by moving detectors. For this purpose, we analyze the Clauser-Horne-Shimony-Holt Bell inequality as a function of the apparatus velocity. Our analysis is motivated by future experiments with entangled photons designed to use satellites. This is a first step toward the implementation of quantum information protocols in a global scale. Entanglement plays a central role in quantum theory as one of its most distinguishing features [1,2]. It allows for the proof that no theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics [3]. As for applications, entanglement is crucial to quantum cryptography [4][5][6], teleportation [7], dense coding [8], and to the conception of quantum computers (see, e.g., Refs. [9,10], and references therein). Currently, there is much interest in testing quantum mechanics for large space distances and eventually in implementing quantum information protocols in global scales [11][12][13][14][15]. Photons seem to be the ideal physical objects for this purpose. Since present technology limits the use of fiber optics in this context up to about 100 km [16], the most viable alternative to go beyond happens to be free-space transmission using satellites and ground stations [17][18][19]. Here, rather than discussing the paramount technical challenges related to these experiments, we focus on an intrinsic physical restriction posed by the motion of the satellites when special relativity is taken into consideration (see also Ref. [20], and references therein). We address this issue by investigating the ClauserHorne-Shimony-Holt (CHSH) Bell inequality [21] for two entangled photons when one of the detectors is boosted with some velocity. Hereafter we assumeh = c = 1 unless stated otherwise.Let us assume a system composed of two photons, A and B, as emitted in opposite directions along the z axis in a SPS cascade [22]. The polarization of photons A and B is measured along arbitrary directions as defined by the unit vectorsâ i andb j (i, j = 1, 2), respectively, which are orthogonal to the z axis. The distance between the two detectors is large enough to make both measurements causally disconnected. It is well known that the CHSH Bell inequalityis satisfied for local hidden variable theories. Hereis the polarization correlation function obtained after an arbitrarily large number N of experiments is performed, and P A n (â i ) assume +1 or −1 values depending on whether the polarization of photon A is measured alongâ i or orthogonally to it, respectively, and analogously for P B n (b j ). Now, we investigate inequality (1) in the context of quantum mechanics when we allow one of the detectors to move along the z axis (say, carried by a satellite). Let us write the normalized state of a two-photon system as [23,24] where s X , andHere, X = A, B distinguishes between both particles, k X = ( k X , k X ) are the corresponding four-momenta, and s X...

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps.