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Special Relativity “Meets” the Uncertainty Principle

Pavle Ilija Premović

Jan 1, 20200 citations

A Discussion on Heisenberg Uncertainty Principle in the Picture of Special Relativity

Luca Nanni

Jan 9, 20150 citations

Fine-Grained Uncertainty Relations for Quantum Testers

Taihei Kimoto

The uncertainty principle is one of the features of quantum theory. Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of this principle. Each FGUR is derived from a scenario where multiple measurements of a quantum state are stochastically performed. While state measurements are fundamental, measuring quantum processes, namely, completely positive and trace preserving maps, is also crucial both theoretically and practically. These measurements are mathematically characterized by quantum testers. In this study, we develop FGURs in terms of quantum testers. Because state preparation is a type of quantum process, our framework encompasses the conventional case as a special instance. The generalized FGURs' bounds are typically challenging to compute. Thus, we also provide estimates for these bounds. Specifically, we explore quantum testers involving maximally entangled states in detail. Consequently, some FGURs for quantum testers are derived as explicit forms for specific settings.The uncertainty principle is one of the features of quantum theory. Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of this principle. Each FGUR is derived from a scenario where multiple measurements of a quantum state are stochastically performed. While state measurements are fundamental, measuring quantum processes, namely, completely positive and trace preserving maps, is also crucial both theoretically and practically. These measurements are mathematically characterized by quantum testers. In this study, we develop FGURs in terms of quantum testers. Because state preparation is a type of quantum process, our framework encompasses the conventional case as a special instance. The generalized FGURs' bounds are typically challenging to compute. Thus, we also provide estimates for these bounds. Specifically, we explore quantum testers involving maximally entangled states in detail. Consequently, some FGURs for quantum testers are derived as explicit forms for specific settings.

arXiv:2409.08542Journal of the Physical Society of JapanApr 4, 20250 citations

Uncertainty relations and approximate quantum error correction

Joseph M. Renes

The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for ``amplitude'' and ``phase'' information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.The uncertainty principle can be understood as constraining the probability of winning a game in which Alice measures one of two conjugate observables, such as position or momentum, on a system provided by Bob, and he is to guess the outcome. Two variants are possible: either Alice tells Bob which observable she measured, or he has to furnish guesses for both cases. Here I derive uncertainty relations for both, formulated directly in terms of Bob's guessing probabilities. For the former these relate to the entanglement that can be recovered by action on Bob's system alone. This gives an explicit quantum circuit for approximate quantum error correction using the guessing measurements for ``amplitude'' and ``phase'' information, implicitly used in the recent construction of efficient quantum polar codes. I also find a relation on the guessing probabilities for the latter game, which has application to wave-particle duality relations.

arXiv:1605.01420Physical Review ASep 14, 201614 citations

Uncertainty Principle and Relativity

B. Kivel

American Journal of PhysicsApr 1, 19600 citations

Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs

Ming‐Liang Hu, Heng Fan

We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states.We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states.

arXiv:1208.1655Physical Review ASep 26, 2012177 citations

Explicit and Implicit Uncertainties and the Uncertainty Principle in the Special Theory of Relativity

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