# Operator-sum representation for bosonic Gaussian channels

@article{Ivan2011OperatorsumRF, title={Operator-sum representation for bosonic Gaussian channels}, author={J. Solomon Ivan and Krishna Kumar Sabapathy and R. Simon}, journal={Physical Review A}, year={2011}, volume={84}, pages={042311} }

Operator-sum or Kraus representations for single-mode bosonic Gaussian channels are developed, and several of their consequences explored. The fact that the two-mode metaplectic operators acting as unitary purification of these channels do not, in their canonical form, mix the position and momentum variables is exploited to present a procedure which applies uniformly to all families in the Holevo classification. In this procedure the Kraus operators of every quantum-limited Gaussian channel can…

## 74 Citations

Divergence free approach for obtaining decompositions of quantum-optical processes

- Physics
- 2018

Operator-sum representations of quantum channels can be obtained by applying the channel to one subsystem of a maximally entangled state and deploying the channel-state isomorphism. However, for…

All phase-space linear bosonic channels are approximately Gaussian dilatable

- Physics, MathematicsNew Journal of Physics
- 2018

We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation…

Linear bosonic quantum channels defined by superpositions

- Computer Science, PhysicsQuantum Inf. Comput.
- 2018

The notion of nonclassicality distance is used to show that the initial environment superposition state becomes maximally non classical as the constraint energy is increased.

Linear bosonic quantum channels defined by superpositions of maximally distinguishable Gaussian environments

- Physics
- 2017

A minimal energy quantum superposition of two maximally distinguishable, isoenergetic single mode Gaussian states is used to construct the system-environment representation of a class of linear…

Efficient representation of Gaussian states for multimode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons

- Mathematics, PhysicsPhysical Review A
- 2019

We introduce a complete description of a multi-mode bosonic quantum state in the coherent-state basis (which in this work is denoted as "$K$" function ), which---up to a phase---is the square root of…

Passive States Optimize the Output of Bosonic Gaussian Quantum Channels

- Mathematics, Computer ScienceIEEE Transactions on Information Theory
- 2016

An ordering between the quantum states emerging from a single-mode gauge-covariant bosonic Gaussian channel is proved and it is shown that within the set of input density matrices with the same given spectrum, the element passive with respect to the Fock basis produces an output, which majorizes all the other outputs emerging from the same set.

Multiparticle quantum interference in Bogoliubov bosonic transformations

- Physics
- 2018

We explore the multiparticle transition probabilities in Gaussian unitaries effected by a twomode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the…

Majorization preservation of Gaussian bosonic channels

- Physics, Mathematics
- 2015

It is shown that phase-insensitive Gaussian bosonic channels are majorization-preserving over the set of passive states of the harmonic oscillator. This means that comparable passive states under…

Some aspects of the interplay between bipartite correlations and quantum channels[HBNI Th65]

- Physics
- 2013

This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various…

Non-Gaussian bosonic channels in the Tavis-Cummings model

- Computer Science, PhysicsQuantum Inf. Process.
- 2019

It is shown that the respective channels are not entanglement breaking, are extremal and can generate both non-classicality and non-Gaussianity.

## References

SHOWING 1-10 OF 123 REFERENCES

Multi-mode bosonic Gaussian channels

- Physics, Mathematics
- 2008

A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a…

Optimal unitary dilation for bosonic Gaussian channels

- Physics, Mathematics
- 2011

A general quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. In this paper the minimal number of quantum Gaussian…

Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1994

It is shown that all conceivable variance matrices can be generated through squeezed thermal states of the n-mode system and their symplectic transforms and developed in both the real and the complex forms for varianceMatrices.

Quantum-mechanical lossless beam splitter: SU(2) symmetry and photon statistics.

- Physics, MedicinePhysical review. A, General physics
- 1989

It is shown that homodyning quantum fluctuations can be reduced by using a balanced photomixer for arbitrary input states.

Gaussian-Wigner distributions in quantum mechanics and optics.

- Physics, MedicinePhysical review. A, General physics
- 1987

The Wigner distribution method is shown to be a convenient framework for characterizing Gaussian kernels and their unitary evolution under Sp(2n,openR) action and the nontrivial role played by a phase term in the kernel is brought out.

Gaussian pure states in quantum mechanics and the symplectic group.

- Physics, MedicinePhysical review. A, General physics
- 1988

Transformation properties of a special class of partially coherent anisotropic Gaussian Schell-model optical fields under the action of Sp(4, openR) first-order systems are worked out, and a generalization of the ``abcd law'' to the partially coherent case is derived.

One-mode bosonic Gaussian channels: a full weak-degradability classification

- Physics
- 2006

A complete degradability analysis of one-mode bosonic Gaussian channels is presented. We show that apart from the class of channels which are unitarily equivalent to the channels with additive…

Quantum characterization of bipartite Gaussian states

- Physics
- 2010

Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the…

Coherent and incoherent states of the radiation field

- Physics
- 1963

Methods are developed for discussing the photon statistics of arbitrary radiation fields in fully quantummechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in…

Quantum limits on bosonic communication rates

- Physics
- 1994

The capacity C of a communication channel is the maximum rate at which information can be transmitted without error from the channel's input to its output. The authors review quantum limits on the…