Influence of detector motion in entanglement measurements with photons

Abstract

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...

Relativistic Bell Test within Quantum Reference Frames

“…If coherence were reduced in the special-relativistic regime, protocols involving the violation of Bell's inequalities would break down for high velocities of the particles, and the special-relativistic corrections in the motion of the particles would result in the introduction of noise. Related to this, there is still ongoing discussion on whether the violation of Bell's inequalities depends on the reference frame: while some authors claim that it is frame independent [12][13][14][15][16][17][18][19], others found it to be frame dependent [20][21][22][23][24][25][26][27][28][29][30][31]. In fact, Lorentz boosts of the full (spin and momentum) state lead in general to a loss of coherence in the reduced spin states of two particles such that different inertial observers seemingly do not agree on the violation of the CHSH-Bell inequality.…”

“…The core of the problem in addressing the question on the violation of Bell's inequalities in the relativistic regime lies in the correct identification of a relativistic spin operator. Several proposals for a relativistic spin operator have been used in the literature to test the violation of Bell's inequalities [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. As a result, it is unknown if one can devise a Bell test for two Dirac particles moving in an arbitrary superposition of relativistic momenta, which would result in a frame-independent statement on the violation of the CHSH-Bell inequality.…”

Bundle Theoretic Descriptions of Massless Single-Particle State Spaces; Gauge Freedom

“…4 The study of massless particles in the context of RQI is still an active area of research (cf. [9,10,[14][15][16][17][18][19][20][21][22][23][24][25][26]). However, to our best knowledge, all the papers that have ever appeared in the literature have used the representation space Eq.…”

Precision in estimating Unruh temperature

“…Concerning inertial quantum systems, we mention the discovery that the reduced entropy of a spin system is not observer invariant [14], fact that has deep implications for the very definition of spin observable [15]. Studies on the Lorentz invariance of entanglement [16,17] and on the behaviour of non-locality [18,19] under relativistic motion were also performed.…”