Fundamental quantum optics experiments conceivable with satellites - reaching relativistic distances and velocities

TLDR: In this article, a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects.

Abstract: Physical theories are developed to describe phenomena in particular regimes, and generally are valid only within a limited range of scales. For example, general relativity provides an effective description of the Universe at large length scales, and has been tested from the cosmic scale down to distances as small as 10 m (Dimopoulos 2007 Phys. Rev. Lett. 98 111102; 2008 Phys. Rev. D 78 042003). In contrast, quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have been performed at the smallest probeable scales at the Large Hadron Collider, ~10−20 m, up to that of hundreds of kilometres (Ursin et al 2007 Nature Phys. 3 481–6). Yet, such tests fall short of the scales required to investigate potentially significant physics that arises at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective, as quantum communication technologies such as quantum key distribution advance into space towards large distances, some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

Figures

Figure 2. Schematic view of a simple Bell-test experiment with entangled photons. Entangled pairs of photons are created in parametric down-conversion of a laser passing through an optical crystal. The entanglement properties of the detected photons are measured in two analyzers. Time-correlation of the photon detection signals is used to identify detections arising from photons that were generated as pairs, typically via a logical AND gate. α and β represent two possible measurement settings for each detector, and N(α, β) the counts corresponding to each pair of settings.

Figure 1. Overview of the distance and velocity scales achievable in a space environment explorable with man-made systems, with some possible quantum optics experiments at each given distance.

Figure 4. From Ref. [30], this spacetime diagram shows the coordinate systems and the locations of the two tests, S1 and S2. The t1 and t2 axes are the world lines of observers who are receding from each other. In each Lorentz frame, the z1 and z2 axes are isochronous: t1 = 0 and t2 = 0, respectively.

Figure 5. Relativistic state transformation as a quantum circuit: the gate D which represents the matrix Dξσ [W (Λ, p)] is controlled by both the classical information and the momentum p, which is itself subject to the classical information (i.e. the Lorentz transformation Λ that relates the reference frames).

Figure 6. Optical COW experiment. The two delays could each be up to 20µs using ∼6 km optical fibres, during which a LEO satellite will move about 15 centimeters. The two beams differ by an angle θ ∼ 31 arc msec.

Figure 3. Effective distance between receivers in an asymmetric Bell experiment. Left: spacetime diagram of the experiment in Alice’s frame, with two measurement events Eg and Es on the ground (Alice) and on a satellite (Bob) respectively. Right: spacetime diagram from perspective of reference frame in which the measurement events Eg and Es are simultaneous. The effective spatial separation of the measurement events X2 is much smaller than the altitude of the orbiting satellite. In each case the green arrow indicates the velocity of the other frame.

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Please do not remove this page
Fundamental quantum optics experiments
conceivable with satellites - Reaching relativistic
distances and velocities
Rideout, David; Jennewein, Thomas; Amelino-Camelia, Giovanni; Demarie, Tommaso; Higgins, Brendon;
Kempf, Achim; Kent, Adrian
https://researchrepository.rmit.edu.au/discovery/delivery/61RMIT_INST:ResearchRepository/12247937590001341?l#13248387180001341
Rideout, Jennewein, T., Amelino-Camelia, G., Demarie, T., Higgins, B., Kempf, A., Kent, A., Laflamme, R., Ma,
X., Mann, R., Martin-Martinez, E., Menicucci, N., Moffat, J., Simon, C., Sorkin, R., Smolin, L., & Terno, D.
(2012). Fundamental quantum optics experiments conceivable with satellites - Reaching relativistic
distances and velocities. Classical and Quantum Gravity, 29(22), 1–44.
https://doi.org/10.1088/0264-9381/29/22/224011
Published Version: https://doi.org/10.1088/0264-9381/29/22/224011
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https://researchbank.rmit.edu.au/view/rmit:34270
A
ccepted Manuscript
2012 IOP Publishing Ltd.
http://dx.doi.org/10.1088/0264-9381/29/22/224011
Rideout, D, Jennewein, T, Amelino-Camelia, G, Demarie, T, Higgins, B, Kempf, A, Kent, A, Laflamme,
R, Ma, X, Mann, R, Martin-Martinez, E, Menicucci, N, Moffat, J, Simon, C, Sorkin, R, Smolin, L and
Terno, D 2012, 'Fundamental quantum optics experiments conceivable with satellites - reaching
relativistic distances and velocities', Classical and Quantum Gravity, vol. 29, no. 22, 224011, pp. 1-44.

Fundamental quantum optics experiments conceivable with satellites —
reaching relativistic distances and velocities
David Rideout
1,2,3 ∗
, Thomas Jennewein
2,4 †
, Giovanni Amelino-Camelia
5
, Tommaso F
Demarie
6
, Brendon L Higgins
2,4
, Achim Kempf
2,3,7
, Adrian Kent
3,8
,
Raymond Laflamme
2,3,4
, Xian Ma
2,4
, Robert B Mann
2,4
, Eduardo Mart´ın-Mart´ınez
2,4
,
Nicolas C Menicucci
3,9
, John Moffat
3
, Christoph Simon
10
, Rafael Sorkin
3
, Lee Smolin
3
,
Daniel R Terno
6
1
current address: Department of Mathematics, University of California / San Diego, La Jolla, CA, USA
∗
E-mail: drideout@math.ucsd.edu
2
Institute for Quantum Computing, Waterloo, ON, Canada
†
E-mail: thomas.jennewein@uwaterloo.ca
3
Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
4
Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada
5
Departimento di Fisica, Universit`a di Roma “La Sapienza”, Rome, Italy
6
Department of Physics and Astronomy, Macquarie University, Sydney, NSW, Australia
7
Department of Applied Mathematics and Department of Physics and Astronomy, University of Waterloo, Waterloo,
ON, Canada
8
Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Cambridge, U.K.
9
School of Physics, The University of Sydney, NSW, Australia
10
Institute for Quantum Information Science and Department of Physics and Astronomy, University of Calgary,
Calgary, AB, Canada
Abstract. Physical theories are developed to describe phenomena in particular regimes, and generally are valid only
within a limited range of scales. For example, general relativity provides an effective description of the Universe at large
length scales, and has been tested from the cosmic scale down to distances as small as 10 meters [1, 2]. In contrast,
quantum theory provides an effective description of physics at small length scales. Direct tests of quantum theory have
been performed at the smallest probeable scales at the Large Hadron Collider, ∼10
−20
meters, up to that of hundreds
of kilometers [3]. Yet, such tests fall short of the scales required to investigate potentially significant physics that arises
at the intersection of quantum and relativistic regimes. We propose to push direct tests of quantum theory to larger and
larger length scales, approaching that of the radius of curvature of spacetime, where we begin to probe the interaction
between gravity and quantum phenomena. In particular, we review a wide variety of potential tests of fundamental physics
that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the
magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum
theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological
models motivated by ideas about spacetime microstructure from quantum gravity. From a more pragmatic perspective,
as quantum communication technologies such as quantum key distribution advance into Space towards large distances,
some of the fundamental physical effects discussed here may need to be taken into account to make such schemes viable.

Fundamental quantum optics experiments conceivable with satellites 2
Contents
1 Introduction 3
1.1 Classification of experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Entanglement tests 7
2.1 Tests of local realism — The “Bell test” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Long distance Bell test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Bell test with human observers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Bell test with detectors in relative motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Bell experiments with macroscopic amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Bimetric gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Relativistic effects in quantum information theory 12
3.1 Special relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Lorentz transformations and polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 General relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.1 Relativistic frame dragging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.2 Entanglement in the presence of curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 The Fermi problem and spacelike entanglement tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4 COW experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 Tests of quantum field theory in non-inertial frames 19
4.1 Test of the Unruh effect, entanglement fidelity and acceleration . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Gravitationally induced entanglement decorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Probe the spacetime structure by spacelike entanglement extraction . . . . . . . . . . . . . . . . . . . . 22
5 Quantum gravity experiments 23
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Lorentz invariant diffusion of polarization from spacetime discreteness . . . . . . . . . . . . . . . . . . . 24
5.2.1 Lorentz invariant diffusion of CMB polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2.2 Testing for spacetime discreteness with satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.3 Decoherence and spacetime noncommutativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.4 “Relativity of Locality” from doubly special relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 Quantum communication and cryptographic schemes 26
6.1 Quantum cryptography with satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.2 Quantum tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.3 Quantum teleportation with satellites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7 Techniques which can be used to gain accuracy or isolate certain effects 28
7.1 Lorentz invariant encodings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7.2 Preparation contextuality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
8 Technology 28
8.1 Measuring the new effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
8.2 Eliminating known sources of noise from the signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
8.3 Proposed systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
9 Conclusion 30
10 Author contributions 30
11 Acknowledgements 31
12 References 31

Fundamental quantum optics experiments conceivable with satellites 3
1. Introduction
Our knowledge is ultimately restricted by the boundaries of what we have explored by direct observation or experiment.
Experiments conducted within previously inaccessible regimes have often revealed new aspects of the Universe,
facilitating new insights into its fundamental operation. Examples of this pervade the history of physical science.
Recently, the theories of general relativity and quantum field theory have arisen to describe aspects of the Universe
that can only be accessed experimentally within the regimes of the very large and the very small, respectively. The
spectacular array of useful technologies brought about owing to the formulation of these theories over the previous
century are vociferous testament to the utility of expanding our experimental horizons.
The success of these two theories also confronts us with a formidable challenge. On one hand, quantum theory
excellently describes the behaviour of physical systems at small length scales. On the other hand, general relativity
theory excellently describes systems involving very large scales: long distances, high accelerations, and massive bodies.†
Each of these theories has successfully weathered copious experimental tests independently, yet the two theories are
famously incompatible in their fundamental assertions. One expects that both theories are limiting cases of one set of
overarching laws of physics. However, the tremendous experimental success of quantum theory and general relativity,
i.e., their enormous individual ranges of validity, makes it extremely difficult to find experimental evidence that points
us towards such unifying laws of physics — a fully quantum theory of gravity.
Theoretical research has yielded intriguing indications about this sought-after unifying theory of quantum gravity.
For example, studies of quantum effects in the presence of black holes, such as Hawking radiation and evaporation,
indicate that it will be crucial to understand how the flow and transformations of information are impacted by relativistic
and quantum effects, with the notion of entanglement playing a central role.
Ultimately, however, the field of quantum gravity will require more experimental guidance. So far, the best potential
for solid experimental evidence for full-blown quantum gravitational effects stems from observations of the cosmic
microwave background (CMB). However, while of the highest interest, the observation of quantum gravity effects in the
CMB would still constitute only a passive one-shot experimental observational opportunity — we cannot repeat the big
bang.
In this paper we thus envisage possible avenues for active experimental probes of quantum phenomena at large
length scales, towards those at which gravitational effects will play an increasingly significant role. The aim in the short
term is to probe more-or-less solid theoretical expectations, while in the longer term to explore physical regimes in which
the predictions of theory are not as clear.
To begin making inroads, it seems necessary to test the behaviour of quantum systems, particularly those with
entanglement, while these systems possess high speeds and are separated by large distances. On Earth, tests of quantum
entanglement have been performed at distances up to 144 km [3]. While this is a significant achievement, it falls short of
the large scale relevant for relativistic considerations. Additionally, these tests were performed with stationary detectors.
While it is difficult to perform tests with moving detectors, it is conceivable to measure entanglement with beamsplitters
moving at up to 1000 m/s (∼10
−6
c) [5]. However, this also falls short — one would need to perform entanglement tests
in which the detectors are in relative motion at speeds nearer lightspeed (c) where relativistic effects become significant.
It is interesting to note that active laboratory measurements of gravity at small scales using atomic interferometers have
also been proposed [1].
Quantum repeater networks are a promising candidate for the long distance dissemination of quantum
entanglement [6]. However, the study of quantum repeaters shows that even with optimistic estimates, reaching 1000 km
will be a huge challenge. Even if quantum transmission technology is developed that is capable of transmitting entangled
systems around the Earth, the maximum separation between detectors that can be achieved is bounded by the Earth’s
diameter: around 13,000 km.
To achieve tests at greater distances and speeds, one needs to move off of planet Earth, and into Space. It
is conceivable that in the not-too-distant future one could perform quantum entanglement tests at the scale of inter-
planetary distances, with the associated velocities. For the nearer term, the next step is to perform quantum experiments
that utilize Earth-orbiting satellite platforms. A satellite in low Earth orbit (LEO), for example, will allow distances
greater than 10
6
m and relative speeds of two detectors of ∼10
−5
c.
Satellite missions for quantum communications have been considered in various configurations [7, 8, 9, 10, 11], and
some scientific tests utilizing such satellites have been proposed. The Canadian Space Agency (CSA) and the Institute
for Quantum Computing (IQC) have been participating in ongoing studies, dubbed QEYSSAT [12], emphasizing the
† At the very smallest of physical scales — the Planck scale — one expects the gravitational interaction to become comparable to all others,
so that quantum and gravitational effects are both simultaneously manifest. The same may also occur at the largest physical scale, that of
the cosmos as a whole, wherein quantum effects may account for formation of large scale structures and the cosmic acceleration [4].

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Fundamental quantum optics experiments conceivable with satellites - reaching relativistic distances and velocities" ?

The authors propose to push direct tests of quantum theory to larger and larger length scales, approaching that of the radius of curvature of spacetime, where they begin to probe the interaction between gravity and quantum phenomena. In particular, the authors review a wide variety of potential tests of fundamental physics that are conceivable with artificial satellites in Earth orbit and elsewhere in the solar system, and attempt to sketch the magnitudes of potentially observable effects. The tests have the potential to determine the applicability of quantum theory at larger length scales, eliminate various alternative physical theories, and place bounds on phenomenological models motivated by ideas about spacetime microstructure from quantum gravity. 

Q2. What are the future works mentioned in the paper "Fundamental quantum optics experiments conceivable with satellites - reaching relativistic distances and velocities" ?

The authors hope that this survey article will stimulate others to further investigate some of these ideas, seriously considering what possibilities for experimental investigation of fundamental physics are, or can be, enabled by these technologies.