Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2014, Volume 47, Issue 41, pp. 415303 - 11

In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and the Golden-Thompson...

von Neumann entropy | squashed entanglement | Golden?Thompson inequality | quantum conditional mutual information | Peierls-Bogoliubov inequality | Golden-Thompson inequality | RELATIVE ENTROPY | INEQUALITIES | PHYSICS, MULTIDISCIPLINARY | EQUALITY | PHYSICS, MATHEMATICAL | Lower bounds | Markov chains | Entanglement | Perturbation methods | Mathematical analysis | Inequalities

von Neumann entropy | squashed entanglement | Golden?Thompson inequality | quantum conditional mutual information | Peierls-Bogoliubov inequality | Golden-Thompson inequality | RELATIVE ENTROPY | INEQUALITIES | PHYSICS, MULTIDISCIPLINARY | EQUALITY | PHYSICS, MATHEMATICAL | Lower bounds | Markov chains | Entanglement | Perturbation methods | Mathematical analysis | Inequalities

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2015, Volume 48, Issue 27, pp. 275303 - 9

We study the relation between the quantum conditional mutual information and the quantum alpha-Renyi divergences. Considering the totally antisymmetric state...

quantum information theory | quantum conditional mutual information | Rényi divergences | non-i.i.d | CAPACITY | RELATIVE ENTROPIES | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | PHYSICS, MATHEMATICAL | Renyi divergences | Markov processes | Mathematical analysis | Failure | Optimization

quantum information theory | quantum conditional mutual information | Rényi divergences | non-i.i.d | CAPACITY | RELATIVE ENTROPIES | PHYSICS, MULTIDISCIPLINARY | ENTANGLEMENT | PHYSICS, MATHEMATICAL | Renyi divergences | Markov processes | Mathematical analysis | Failure | Optimization

Journal Article

Foundations of Physics, ISSN 0015-9018, 08/2018, Volume 48, Issue 8, pp. 910 - 924

Squashed entanglement (Christandl and Winter in J. Math. Phys. 45(3):829-840, 2004) is a monogamous entanglement measure, which implies that highly extendible...

Quantum mutual information | Entanglement | Quantum information theory | RELATIVE ENTROPY | STATES | CONTINUITY | PHYSICS, MULTIDISCIPLINARY | CONDITIONAL MUTUAL INFORMATION | SYSTEMS | STRONG SUBADDITIVITY | ERROR-CORRECTION | Markov processes | Quantum computing | Research | Mathematical research

Quantum mutual information | Entanglement | Quantum information theory | RELATIVE ENTROPY | STATES | CONTINUITY | PHYSICS, MULTIDISCIPLINARY | CONDITIONAL MUTUAL INFORMATION | SYSTEMS | STRONG SUBADDITIVITY | ERROR-CORRECTION | Markov processes | Quantum computing | Research | Mathematical research

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2017, Volume 63, Issue 8, pp. 5360 - 5371

We introduce and analyze a task in which a tripartite quantum state is transformed to an approximately recoverable state by a randomizing operation on one of...

conditional quantum mutual information | Quantum computing | Tensile stress | quantum Markov chain | Quantum mechanics | Focusing | Markov processes | Informatics | Approximate recoverability | CONTINUITY | MARKOV-CHAINS | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENTROPY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Energy levels (Quantum mechanics) | Stochastic processes | Research | Quantum theory | Strength of materials | Tensors | Randomness | Minimum cost | Cost analysis | Recovery | Cost engineering | Subsystems | Physics - Quantum Physics

conditional quantum mutual information | Quantum computing | Tensile stress | quantum Markov chain | Quantum mechanics | Focusing | Markov processes | Informatics | Approximate recoverability | CONTINUITY | MARKOV-CHAINS | INFORMATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENTROPY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Energy levels (Quantum mechanics) | Stochastic processes | Research | Quantum theory | Strength of materials | Tensors | Randomness | Minimum cost | Cost analysis | Recovery | Cost engineering | Subsystems | Physics - Quantum Physics

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 05/2015, Volume 471, Issue 2177, p. 20140941

Characterizing genuine multipartite quantum correlations in quantum physical systems has historically been a challenging problem in quantum information theory....

Multipartite quantum correlation | Quantum Markov chains | Conditional quantum mutual information | Conditional entanglement of multipartite information | Multipartite symmetric quantum discord | multipartite quantum correlation | quantum Markov chains | conditional entanglement of multipartite information | conditional quantum mutual information | RELATIVE ENTROPY | CONTINUITY | STATES | MECHANICAL ENTROPY | INFORMATION | MULTIDISCIPLINARY SCIENCES | SQUASHED ENTANGLEMENT | multipartite symmetric quantum discord | 157 | 158 | 159 | 1009

Multipartite quantum correlation | Quantum Markov chains | Conditional quantum mutual information | Conditional entanglement of multipartite information | Multipartite symmetric quantum discord | multipartite quantum correlation | quantum Markov chains | conditional entanglement of multipartite information | conditional quantum mutual information | RELATIVE ENTROPY | CONTINUITY | STATES | MECHANICAL ENTROPY | INFORMATION | MULTIDISCIPLINARY SCIENCES | SQUASHED ENTANGLEMENT | multipartite symmetric quantum discord | 157 | 158 | 159 | 1009

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 02/2018, Volume 81, Issue 1, pp. 81 - 104

We describe a modification of the Alicki—Fannes—Winter method which allows to prove uniform continuity on the set of quantum states with bounded energy of any...

von Neumann entropy | quantum state | quantum channel | Hamiltonian of a quantum system | quantum mutual information | DIMENSIONAL QUANTUM-SYSTEMS | CAPACITY | ENTANGLEMENT MEASURES | INFORMATION | CONDITIONAL ENTROPY | PHYSICS, MATHEMATICAL | RELATIVE ENTROPY | CONTINUITY

von Neumann entropy | quantum state | quantum channel | Hamiltonian of a quantum system | quantum mutual information | DIMENSIONAL QUANTUM-SYSTEMS | CAPACITY | ENTANGLEMENT MEASURES | INFORMATION | CONDITIONAL ENTROPY | PHYSICS, MATHEMATICAL | RELATIVE ENTROPY | CONTINUITY

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 04/2018, Volume 51, Issue 15

Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy...

von Neumann entropy | CAPACITY | entanglement measures | quantum conditional mutual information | quantum capacity | CHANNEL | PHYSICS, MULTIDISCIPLINARY | quantum relative entropy | convex optimization | CONDITIONAL MUTUAL INFORMATION | PHYSICS, MATHEMATICAL

von Neumann entropy | CAPACITY | entanglement measures | quantum conditional mutual information | quantum capacity | CHANNEL | PHYSICS, MULTIDISCIPLINARY | quantum relative entropy | convex optimization | CONDITIONAL MUTUAL INFORMATION | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2018, Volume 51, Issue 15, p. 154003

Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy...

von Neumann entropy | convex optimization | entanglement measures | quantum capacity | quantum conditional mutual information | quantum relative entropy | CAPACITY | CHANNEL | PHYSICS, MULTIDISCIPLINARY | CONDITIONAL MUTUAL INFORMATION | PHYSICS, MATHEMATICAL | Quantum Physics | Physics

von Neumann entropy | convex optimization | entanglement measures | quantum capacity | quantum conditional mutual information | quantum relative entropy | CAPACITY | CHANNEL | PHYSICS, MULTIDISCIPLINARY | CONDITIONAL MUTUAL INFORMATION | PHYSICS, MATHEMATICAL | Quantum Physics | Physics

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2016, Volume 207, Issue 5, pp. 93 - 142

Several important measures of correlations of the state of a finite-dimensional composite quantum system are defined as linear combinations of marginal...

Marginal entropy | Quantum mutual information | Von neumann entropy | Entanglement-assisted capacity | Quantum channel | CAPACITY | STATES | entanglement-assisted capacity | quantum channel | STRONG SUBADDITIVITY | MATHEMATICS | von Neumann entropy | CONTINUITY | SQUASHED ENTANGLEMENT | CONDITIONAL MUTUAL INFORMATION | marginal entropy | quantum mutual information | ENTROPY | Functions (mathematics) | Concretes | Reproduction | Correlation analysis | Mathematical analysis | Entropy | Channels | Quantum theory

Marginal entropy | Quantum mutual information | Von neumann entropy | Entanglement-assisted capacity | Quantum channel | CAPACITY | STATES | entanglement-assisted capacity | quantum channel | STRONG SUBADDITIVITY | MATHEMATICS | von Neumann entropy | CONTINUITY | SQUASHED ENTANGLEMENT | CONDITIONAL MUTUAL INFORMATION | marginal entropy | quantum mutual information | ENTROPY | Functions (mathematics) | Concretes | Reproduction | Correlation analysis | Mathematical analysis | Entropy | Channels | Quantum theory

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2019, Volume 52, Issue 1, p. 14001

We obtain continuity bounds for basic information characteristics of quantum channels depending on their input dimension (if it is finite) and on the input...

quantum conditional mutual information | quantum channel capacities | ensemble of quantum states | energy-constrained Bures distance | the Holevo quantity | multi-mode quantum oscillator | strong convergence of quantum channels | DISTANCE | PHYSICS, MULTIDISCIPLINARY | CLASSICAL CAPACITY | PHYSICS, MATHEMATICAL | ADDITIVITY | ENTROPY

quantum conditional mutual information | quantum channel capacities | ensemble of quantum states | energy-constrained Bures distance | the Holevo quantity | multi-mode quantum oscillator | strong convergence of quantum channels | DISTANCE | PHYSICS, MULTIDISCIPLINARY | CLASSICAL CAPACITY | PHYSICS, MATHEMATICAL | ADDITIVITY | ENTROPY

Journal Article

New Journal of Physics, ISSN 1367-2630, 08/2015, Volume 17, Issue 8, p. 83019

In this paper, we discuss the connection between two genuinely quantum phenomena-the discontinuity of quantum maximum entropy inference and quantum phase...

numerical range | quantum phase transition | quantum conditional mutual information | maximum entropy inference | STATE | PHYSICS, MULTIDISCIPLINARY | Phase transitions | Entropy | Discontinuity | Phase transformations | Transition points | Inference | Ground state | Maximum entropy | Density | Indicators

numerical range | quantum phase transition | quantum conditional mutual information | maximum entropy inference | STATE | PHYSICS, MULTIDISCIPLINARY | Phase transitions | Entropy | Discontinuity | Phase transformations | Transition points | Inference | Ground state | Maximum entropy | Density | Indicators

Journal Article

Quantum Information Processing, ISSN 1570-0755, 12/2018, Volume 17, Issue 12, pp. 1 - 29

We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that...

Quantum Computing | Finite-dimensional subchannel | Energy constraint | Energy-constrained diamond norm | Mathematical Physics | Quantum conditional mutual information | Quantum Information Technology, Spintronics | Quantum Physics | Physics | Strong convergence of channels | Data Structures and Information Theory | m -Restricted capacities | m-Restricted capacities | QUANTUM INFORMATION | CONTINUITY | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | CONDITIONAL ENTROPY | PHYSICS, MATHEMATICAL

Quantum Computing | Finite-dimensional subchannel | Energy constraint | Energy-constrained diamond norm | Mathematical Physics | Quantum conditional mutual information | Quantum Information Technology, Spintronics | Quantum Physics | Physics | Strong convergence of channels | Data Structures and Information Theory | m -Restricted capacities | m-Restricted capacities | QUANTUM INFORMATION | CONTINUITY | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | CONDITIONAL ENTROPY | PHYSICS, MATHEMATICAL

Journal Article

13.
Contrasting distributions of pairwise entanglement and mutual information in Heisenberg spin systems

International Journal of Quantum Information, ISSN 0219-7499, 09/2016, Volume 14, Issue 6

The correlations between a pair of spins in a many-spin state encoded in the diagonal and off-diagonal spin-spin correlation functions. These spin functions...

conditional entrap | concurrence | Quantum correlation | spin systems | COMPUTER SCIENCE, THEORY & METHODS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

conditional entrap | concurrence | Quantum correlation | spin systems | COMPUTER SCIENCE, THEORY & METHODS | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 08/2018, Volume 51, Issue 37, p. 374001

We consider entanglement-assisted (EA) private communication over a quantwn broadcast channel, in which there is a single sender and multiple receivers. We...

conditional mutual information | quantum broadcast channels | entanglement-assisted private communication | 2ND-ORDER ASYMPTOTICS | PHYSICS, MULTIDISCIPLINARY | INFORMATION | CLASSICAL CAPACITY | CONVERSE BOUNDS | ENTROPIES | PHYSICS, MATHEMATICAL | KEY | Physics - Quantum Physics

conditional mutual information | quantum broadcast channels | entanglement-assisted private communication | 2ND-ORDER ASYMPTOTICS | PHYSICS, MULTIDISCIPLINARY | INFORMATION | CLASSICAL CAPACITY | CONVERSE BOUNDS | ENTROPIES | PHYSICS, MATHEMATICAL | KEY | Physics - Quantum Physics

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2016, Volume 62, Issue 4, pp. 1758 - 1763

Fawzi and Renner recently established a lower bound on the conditional quantum mutual information (CQMI) of tripartite quantum states ABC in terms of the...

Minimization | Correlation | Entropy | Quantum entanglement | Quantum Mechanics | Information theory | Quantum Entanglement | Information Theory | entropy | OPTIMAL QUANTUM | Quantum mechanics | quantum entanglement | SQUASHED ENTANGLEMENT | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONDITIONAL MUTUAL INFORMATION | information theory | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical optimization | Entropy (Information theory)

Minimization | Correlation | Entropy | Quantum entanglement | Quantum Mechanics | Information theory | Quantum Entanglement | Information Theory | entropy | OPTIMAL QUANTUM | Quantum mechanics | quantum entanglement | SQUASHED ENTANGLEMENT | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONDITIONAL MUTUAL INFORMATION | information theory | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Mathematical optimization | Entropy (Information theory)

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2017, Volume 107, Issue 12, pp. 2239 - 2265

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all...

Measured relative entropy | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantum entropy | Physics | Geometry | 81Q99 | Convex optimization | 15A45 | Relative entropy of recovery | 94A17 | Group Theory and Generalizations | Additivity in quantum information theory | Operator Jensen inequality | STATES | ENTANGLEMENT | INEQUALITY | PHYSICS, MATHEMATICAL | PROBABILITY | CONDITIONAL MUTUAL INFORMATION | LIEB | Atoms | Quantum Physics

Measured relative entropy | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantum entropy | Physics | Geometry | 81Q99 | Convex optimization | 15A45 | Relative entropy of recovery | 94A17 | Group Theory and Generalizations | Additivity in quantum information theory | Operator Jensen inequality | STATES | ENTANGLEMENT | INEQUALITY | PHYSICS, MATHEMATICAL | PROBABILITY | CONDITIONAL MUTUAL INFORMATION | LIEB | Atoms | Quantum Physics

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 02/2016, Volume 472, Issue 2186, p. 20150623

A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery...

Quantum Markov chains | Strong subadditivity | Recoverability | Conditional mutual information | conditional mutual information | quantum Markov chains | RELATIVE ENTROPY | QUANTUM-MECHANICAL ENTROPY | STATES | FIDELITY | recoverability | MULTIDISCIPLINARY SCIENCES | ASYMPTOTICS | strong subadditivity | Quantum Physics | Physics | 157 | 159 | 1009 | 120

Quantum Markov chains | Strong subadditivity | Recoverability | Conditional mutual information | conditional mutual information | quantum Markov chains | RELATIVE ENTROPY | QUANTUM-MECHANICAL ENTROPY | STATES | FIDELITY | recoverability | MULTIDISCIPLINARY SCIENCES | ASYMPTOTICS | strong subadditivity | Quantum Physics | Physics | 157 | 159 | 1009 | 120

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 6/2013, Volume 52, Issue 6, pp. 2112 - 2117

A simpler approach to the characterization of vanishing conditional mutual information is presented. Some remarks are given as well. More specifically,...

Commutator | Von Neumann entropy | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Strong subadditivity (SSA) | Physics | Conditional mutual information | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | QUANTUM ENTROPY | STRONG SUBADDITIVITY | Markov processes | Analysis

Commutator | Von Neumann entropy | Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics, general | Strong subadditivity (SSA) | Physics | Conditional mutual information | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | QUANTUM ENTROPY | STRONG SUBADDITIVITY | Markov processes | Analysis

Journal Article

19.
Full Text
Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2015, Volume 48, Issue 50, pp. 505301 - 26

A short quantum Markov chain is a tripartite state rho(ABC) such that system A can be recovered perfectly by acting on system C of the reduced state. rho(BC)...

Rényi conditional mutual information | quantum Markov chain | sufficiency of channels | Renyi conditional mutual information | CAPACITY | STRONG CONVERSE | INEQUALITIES | CONCAVITY | PHYSICS, MULTIDISCIPLINARY | PROPERTY | STRONG SUBADDITIVITY | PHYSICS, MATHEMATICAL | RELATIVE ENTROPY | ALGEBRAS | MECHANICAL ENTROPY | EQUALITY | Markov chains | Entropy | Mathematical analysis | Recovery | Channels

Rényi conditional mutual information | quantum Markov chain | sufficiency of channels | Renyi conditional mutual information | CAPACITY | STRONG CONVERSE | INEQUALITIES | CONCAVITY | PHYSICS, MULTIDISCIPLINARY | PROPERTY | STRONG SUBADDITIVITY | PHYSICS, MATHEMATICAL | RELATIVE ENTROPY | ALGEBRAS | MECHANICAL ENTROPY | EQUALITY | Markov chains | Entropy | Mathematical analysis | Recovery | Channels

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 9/2011, Volume 306, Issue 3, pp. 805 - 830

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | RELATIVE ENTROPY | STRONG CONVERSE | THEOREM | DISTILLATION | COMPLEXITY | SYSTEMS | STRONG SUBADDITIVITY | CONDITIONAL INFORMATION | PHYSICS, MATHEMATICAL | QUANTUM SEPARABILITY PROBLEM | MIXED-STATE ENTANGLEMENT | Atoms | Algorithms | Physics - Quantum Physics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | RELATIVE ENTROPY | STRONG CONVERSE | THEOREM | DISTILLATION | COMPLEXITY | SYSTEMS | STRONG SUBADDITIVITY | CONDITIONAL INFORMATION | PHYSICS, MATHEMATICAL | QUANTUM SEPARABILITY PROBLEM | MIXED-STATE ENTANGLEMENT | Atoms | Algorithms | Physics - Quantum Physics

Journal Article

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