Strong subadditivity for log-determinant of covariance matrices and its applications
arXiv:1601.03226 · doi:10.1088/1751-8113/49/34/34LT02
Abstract
We prove that the log-determinant of the covariance matrix obeys the strong subadditivity inequality for arbitrary tripartite states of multimode continuous variable quantum systems. This establishes general limitations on the distribution of information encoded in the second moments of canonically conjugate operators. The inequality is shown to be stronger than the conventional strong subadditivity inequality for von Neumann entropy in a class of pure tripartite Gaussian states. We finally show that such an inequality implies a strict monogamy-type constraint for joint Einstein-Podolsky-Rosen steerability of single modes by Gaussian measurements performed on multiple groups of modes.
12 pages, 2 figures. To appear in J. Phys. A: Math. Theor
References in corpus (17)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Quantum information can be negative
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantification of Gaussian quantum steering
- Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
- Multiphoton Quantum Optics and Quantum State Engineering
- Observation of genuine one-way Einstein-Podolsky-Rosen steering
- Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
- Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
- Full characterization of Gaussian bipartite entangled states by a single homodyne detector
- Gaussian quantum marginal problem
- Einstein-Podolsky-Rosen steering measure for two-mode continuous variable states
- Quantum steering of Gaussian states via non-Gaussian measurements
- Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
- Experimentally friendly bounds on non-Gaussian entanglement from second moments
- Operational Quantification of Continuous Variable Correlations
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- Quantum Steering
- Multipartite Gaussian steering: monogamy constraints and quantum cryptography applications
- Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states
- Schur complement inequalities for covariance matrices and monogamy of quantum correlations
- Versatile Multipartite Einstein-Podolsky-Rosen Steering via a Quantum Frequency Comb
- From log-determinant inequalities to Gaussian entanglement via recoverability theory
- Non-classical correlations in quantum mechanics and beyond
- Quantification of Wigner Negativity Remotely Generated via Einstein-Podolsky-Rosen Steering
- Extendibility of bosonic Gaussian states
- On the Strong Subadditivity of the Rényi entropies for bosonic and fermionic Gaussian states
- Page curves and typical entanglement in linear optics
- Shareability of steering in 2-producible states
- Demonstration of monogamy laws for Gaussian steering in optomechanics
- Fundamental limitations to key distillation from Gaussian states with Gaussian operations
- Understanding Neural Networks with Logarithm Determinant Entropy Estimator