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arXiv:2306.08136 · Physical Review A

Unveiling quantum complementarity tradeoffs in relativistic scenarios

Marcos L. W. Basso, Ismael L. Paiva, Pedro R. Dieguez

Published Jun 4, 2024• 1 citation
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Abstract

Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the system's external degrees of freedom. To conduct our study, we utilize two generalized delayed-choice interferometers. Despite differences in complementarity tradeoffs inside the interferometers, the interferometric visibility of both setups coincides in any relativistic regime. Our results extend the finding that general relativity induces a universal decoherence effect on quantum superpositions, as local Wigner rotations, being purely kinematical, preclude any spin dynamics. To illustrate, we analyze the Newtonian limit of our results.

DOI
10.1103/physreva.109.062207

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Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with an internal spin. This effect stems from local Wigner rotations in the spacetime, which couple the spin to the system's external degrees of freedom. To conduct our study, we utilize two generalized delayed-choice interferometers. Despite differences in complementarity tradeoffs inside the interferometers, the interferometric visibility of both setups coincides in any relativistic regime. Our results extend the finding that general relativity induces a universal decoherence effect on quantum superpositions, as local Wigner rotations, being purely kinematical, preclude any spin dynamics. To illustrate, we analyze the Newtonian limit of our results.
Delayed-choice experiments challenge classical intuitions by allowing the configuration of an interferometer to be chosen after a quantum system has already entered it. While these experiments support Bohr’s complementarity principle, the introduction of quantum control reveals that the manifestation of complementarity depends critically on the full physical context — including quantum correlations and the causal order of operations. In this work, we propose and analyze a modified entanglement-assisted delayed-choice experiment that maintains the same final visibility as the standard setup but reverses its causal structure. Here, we go beyond output statistics to examine how wave-particle realism evolves throughout the interferometer. Using a contextual realism quantifier, we show that wave and particle realism can be meaningfully assigned at intermediate stages with a clear connection with the final interferometric visibility. Specifically, our results show that modifying the causal order of operations and information structure, whether through entanglement tuning or post-selection, leads to significant variations in the wave-particle complementarity relation.
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. In the theory of general relativity time flows at different rates depending on the space–time geometry. Here, a drop in the visibility of a quantum 'clock' interference in a gravitational potential is predicted, which cannot be explained without the general relativistic notion of time.
Abstract Quantum delayed-choice experiments are designed to probe the robustness of the complementarity principle. In this proceeding, we revisit the main ideas reported recently in Ref. [Commun. Phys. 5, 82 (2022)] concerning a setup (quantum-controlled reality experiment) that has the same final visibility as the quantum version of Wheeler’s delayed-choice arrangement. Besides the same final statistics, upon an operational criterion of physical realism, the authors claimed a different state of affairs for the wave-and-particle behavior in delayed-choice experiments. To this end, we put forward an analysis by employing the relative entropy of coherence to study how the local wave and particle coherences when the system is traveling inside the interferometer change accordingly to the final observed visibility.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by violating Bell inequalities. While the role of entanglement is well studied in the realm of nonrelativistic quantum mechanics, its significance in a relativistic quantum theory is a relatively new field of interest. In this work the consequences of a relativistic description of quantum entanglement are discussed. We analyze the representations of the symmetry groups of special relativity, i.e. of the Lorentz group, and the Poincaré group, on the Hilbert space of states. We describe how unitary, irreducible representations of the Poincaré group for massive spin 1/2 particles are constructed from representations of Wigner's little group. We then proceed to investigate the role of the Wigner rotations in the transformation of quantum states under a change of inertial reference frame. Considering different partitions of the Hilbert space of 2 particles, we find that the entanglement of the quantum states appears different in different inertial frames, depending on the form of the states, the chosen inertial frames, and the particular choice of partition. It is explained, how, despite of this, the maximally possible violation of Bell inequalities is frame independent, when using appropriate spin observables, which are related to the Pauli-Ljubanski vector, a Casimir operator of the Poincaré group.
A recent analysis by Pikovski et al. [Nat. Phys. 11, 668 (2015)] has triggered interest in the question of how to include relativistic corrections in the quantum dynamics governing many-particle systems in a gravitational field. Here we show how the center-of-mass motion of a quantum system subject to gravity can be derived more rigorously, addressing the ambiguous definition of relativistic center-of-mass coordinates. We further demonstrate that, contrary to the prediction by Pikovski et al., external forces play a crucial role in the relativistic coupling of internal and external degrees of freedom, resulting in a complete cancellation of the alleged coupling in Earth-bound laboratories for systems supported against gravity by an external force. We conclude that the proposed decoherence effect is an effect of relative acceleration between quantum system and measurement device, rather than a universal effect in gravitational fields.
We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we investigate the behavior of these different complementary properties of massive spin-1/21/21/2 particles in the Schwarzschild spacetime. For geodetic circular orbits, we find that the spin state of one particle oscillates between a separable and an entangled state. For nongeodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit nears the Schwarzschild radius rs{r}_{s}rs​.