Interconversion of pure Gaussian states using non-Gaussian operations

Abstract

We analyze the conditions under which local operations and classical communication enable entanglement transformations within the set of bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found in [Quant. Inf. Comp. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 x 2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.

arXiv comment9 pages, 3 figures

References in corpus (20)

• Quantum entanglement
• Quantum information with continuous variables
• The Security of Practical Quantum Key Distribution
• Gaussian Quantum Information
• Bell nonlocality
• Quantum Teleportation is a Universal Computational Primitive
• Cool horizons for entangled black holes
• Conditions for a class of entanglement transformations
• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Experimental Demonstration of Blind Quantum Computing
• Gaussian transformations and distillation of entangled Gaussian states
• A No-Go Theorem for Gaussian Quantum Error Correction
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Quantum state majorization at the output of bosonic Gaussian channels
• Majorization theory approach to the Gaussian channel minimum entropy conjecture
• Conditions for the local manipulation of Gaussian states
• Strong no-go theorem for Gaussian quantum bit commitment
• Majorization relations and entanglement generation in a beam splitter
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication

Cited by in corpus (6)

• Resource theory of quantum non-Gaussianity and Wigner negativity
• Majorization uncertainty relations for mixed quantum states
• Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator
• Quantum Hypergraph States in Continuous Variables
• Majorization preservation of Gaussian bosonic channels
• Fock majorization in bosonic quantum channels with a passive environment