# Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels

@inproceedings{Palma2017MultimodeGO, title={Multimode Gaussian optimizers for the Wehrl entropy and quantum Gaussian channels}, author={Giacomo De Palma and Dario Trevisan and Vittorio Giovannetti}, year={2017} }

We prove in the multimode scenario a fundamental relation between the Wehrl and the von Neumann entropy, stating that the minimum Wehrl entropy among all the quantum states with a given von Neumann entropy is achieved by thermal Gaussian states. We also prove that thermal Gaussian input states minimize the output von Neumann entropy of multimode quantum Gaussian attenuators, amplifiers and phase-contravariant channels among all the input states diagonal in some product basis and with a given…

## 11 Citations

### New Lower Bounds to the Output Entropy of Multi-Mode Quantum Gaussian Channels

- Computer Science, PhysicsIEEE Transactions on Information Theory
- 2019

We prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode…

### New lower bounds to the output entropy of multi-mode quantum Gaussian channels

- Computer Science, PhysicsIEEE Trans. Inf. Theory
- 2019

We prove that quantum thermal Gaussian input states minimize the output entropy of the multi-mode quantum Gaussian attenuators and amplifiers that are entanglement breaking and of the multi-mode…

### Uncertainty relations with quantum memory for the Wehrl entropy

- Physics, Computer ScienceArXiv
- 2017

Two new fundamental uncertainty relations with quantum memory for the Wehrl entropy are proved and will be a valuable tool in quantum information and will find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics.

### Uncertainty relations with quantum memory for the Wehrl entropy

- Physics, Computer ScienceLetters in Mathematical Physics
- 2018

Two new fundamental uncertainty relations with quantum memory for the Wehrl entropy are proved and will be a valuable tool in quantum information and will find application in security proofs of quantum key distribution protocols in the asymptotic regime and in entanglement witnessing in quantum optics.

### Gaussian optimizers for entropic inequalities in quantum information

- Computer Science, PhysicsJournal of Mathematical Physics
- 2018

It is shown that the restriction of the quantum-limited Gaussian attenuator to input states diagonal in the Fock basis coincides with the thinning, the analogue of the rescaling for positive integer random variables.

### The Conditional Entropy Power Inequality for Bosonic Quantum Systems

- Computer Science
- 2017

The conditional Entropy Power Inequality for Gaussian quantum systems is proved, based on a new Stam inequality for the quantum conditional Fisher information and on the determination of the universal asymptotic behaviour of the Quantum conditional entropy under the heat semigroup evolution.

### The Entropy Power Inequality with quantum memory

- Computer Science, PhysicsArXiv
- 2017

The Entropy Power Inequality for Gaussian quantum systems in the presence of quantum memory is proved and will have a strong impact in quantum information and quantum cryptography, and is exploited to prove an upper bound to the entanglement-assisted classical capacity of a non-Gaussian quantum channel.

### The conditional Entropy Power Inequality for quantum additive noise channels

- Computer Science, MathematicsJournal of Mathematical Physics
- 2018

It is proved that the quantum conditional Entropy Power Inequality is optimal in the sense that it can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states.

### The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier

- PhysicsJournal of Mathematical Physics
- 2019

We determine the maximum squashed entanglement achievable between sender and receiver of the noiseless quantum Gaussian attenuators and amplifiers and we prove that it is achieved sending half of an…

### The Entropy Power Inequality with quantum conditioning

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2019

The conditional entropy power inequality is proved in the scenario where the conditioning system is quantum, based on the heat semigroup and on a generalization of the Stam inequality in the presence of quantum conditioning.

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