Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Symposium on Information Theory (ISIT)

Uncertainty Principle for Quantum Channels

Li Gao, Marius Junge, Nicholas D. LaRacuente

Published Jun 1, 2018• 11 citations
Publisher

Abstract

We extend the quantum entropic uncertainty principle beyond measurements, to a pair of finite-dimensional quantum channels acting on the same input system. This also generalizes strong super-additivity inequality by giving a lower bound on generalizations of conditional mutual information. Moreover we show that the corresponding “squashed” conditional mutual information is additive in this general setting.

DOI
10.1109/isit.2018.8437730

Related papers

Entropy Uncertainty Relations and Strong Sub-additivity of Quantum Channels

Gao, Li, Marius Junge, Nicholas D. LaRacuente

We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized SSA for quantum relative entropy. As a special case, it gives an improved data processing inequality.

arXiv:2301.08402•Jan 20, 2023•0 citations

On Lower Semicontinuity of the Quantum Conditional Mutual Information and Its Corollaries

Максим Евгеньевич Широков

Abstract It is shown that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence topology). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably indecomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities with respect to perturbation of the measurement and the measured state.

arXiv:2001.08691•Proceedings of the Steklov Institute of Mathematics•Jul 1, 2021•5 citations

Entropic uncertainty relation and strong subadditvity of quantum channels

Gao Li, Marius Junge, Nicholas D. LaRacuente

We extend the entropic uncertainty principle from quantum measurements to quantum channels. This is obtained via a generalized strong subadditivity (SSA) of quantum entropy. Motivated by Petz's algebraic SSA inequality, we also obtain a generalized strong subadditivity of quantum relative entropy. The English version of this article is available at arXiv:2301.08402.

Scientia Sinica Mathematica•Jun 26, 2023•0 citations

Strong Subadditivity Inequality and Entropic Uncertainty Relations

Li Gao, Marius Junge, Nicholas D. LaRacuente

We prove a generalization of the strong-subadditivity (SSA) inequality in the context of finite dimensional von Neumann algebras. Our generalized SSA inequality subsumes various entropic uncertainty relations, such as the Maassen-Uffink inequality in the presence of quantum memory. Motivated by the generalization of SSA, we introduce an analog of conditional mutual information and discuss superadditivity and monotonicity under certain operations. Our proof uses complex interpolation and noncommutative mixed $L_p$ spaces.

•Oct 27, 2017•8 citations

Tightening the entropic uncertainty bound in the presence of quantum memory

Farzin Adabi, S. Salimi, Soroush Haseli

The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables cannot be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. M. Berta et al. [Nat. Phys. 6, 659 (2010)] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on the Holevo quantity and mutual information. We conclude that our lower bound will be tightened with respect to that of Berta et al. when the accessible information about measurements outcomes is less than the mutual information about the joint state. Some examples have been investigated for which our lower bound is tighter than Berta et al.'s lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has been obtained, as well as an upper bound for the regularized distillable common randomness.

arXiv:1602.04296•Physical Review A•Jun 23, 2016•142 citations

Controlling the entropic uncertainty lower bound in two-qubit systems under decoherence

S Haseli, Hazhir Dolatkhah, S. Salimi +1 more

Abstract The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various forms. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is Shannon’s entropy. In this work, we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory. Alice measures on her particle A and Bob, with memory particle B , predicts Alice’s measurement outcomes. It has a wide range of applications, for example, entanglement witnessing and quantum key distribution. We study the effects of the environment on the entropic uncertainty lower bound in the presence of weak measurement and measurement reversal. The dynamical model that is intended in this work is as follows: first the weak measurement is performed, second, the decoherence affects the system and finally the measurement reversal is performed on the quantum system. Here, we consider the generalized amplitude damping channel and depolarizing channel as environmental noises. We will show that in the presence of weak measurement and measurement reversal, despite the presence of environmental factors, the entropic uncertainty lower bound drops to an optimal minimum value. In fact, weak measurement and measurement reversal enhance the quantum correlation between the subsystems A and B , and thus the uncertainty of Bob regarding Alice’s measurement outcomes reduces. Based on the entropic uncertainty relation, one can also show that the weak measurement and measurement reversal can preserve the quantum secret key rate lower bound from decoherence.

arXiv:1808.01600•Laser Physics Letters•Mar 29, 2019•23 citations
We extend the quantum entropic uncertainty principle beyond measurements, to a pair of finite-dimensional quantum channels acting on the same input system. This also generalizes strong super-additivity inequality by giving a lower bound on generalizations of conditional mutual information. Moreover we show that the corresponding “squashed” conditional mutual information is additive in this general setting.
Abstract It is shown that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence topology). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably indecomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities with respect to perturbation of the measurement and the measured state.
We prove a generalization of the strong-subadditivity (SSA) inequality in the context of finite dimensional von Neumann algebras. Our generalized SSA inequality subsumes various entropic uncertainty relations, such as the Maassen-Uffink inequality in the presence of quantum memory. Motivated by the generalization of SSA, we introduce an analog of conditional mutual information and discuss superadditivity and monotonicity under certain operations. Our proof uses complex interpolation and noncommutative mixed LpL_pLp​ spaces.
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables cannot be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. M. Berta et al. [Nat. Phys. 6, 659 (2010)] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on the Holevo quantity and mutual information. We conclude that our lower bound will be tightened with respect to that of Berta et al. when the accessible information about measurements outcomes is less than the mutual information about the joint state. Some examples have been investigated for which our lower bound is tighter than Berta et al.'s lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has been obtained, as well as an upper bound for the regularized distillable common randomness.
Abstract The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various forms. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is Shannon’s entropy. In this work, we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory. Alice measures on her particle A and Bob, with memory particle B , predicts Alice’s measurement outcomes. It has a wide range of applications, for example, entanglement witnessing and quantum key distribution. We study the effects of the environment on the entropic uncertainty lower bound in the presence of weak measurement and measurement reversal. The dynamical model that is intended in this work is as follows: first the weak measurement is performed, second, the decoherence affects the system and finally the measurement reversal is performed on the quantum system. Here, we consider the generalized amplitude damping channel and depolarizing channel as environmental noises. We will show that in the presence of weak measurement and measurement reversal, despite the presence of environmental factors, the entropic uncertainty lower bound drops to an optimal minimum value. In fact, weak measurement and measurement reversal enhance the quantum correlation between the subsystems A and B , and thus the uncertainty of Bob regarding Alice’s measurement outcomes reduces. Based on the entropic uncertainty relation, one can also show that the weak measurement and measurement reversal can preserve the quantum secret key rate lower bound from decoherence.