Conversion of Gaussian states under incoherent Gaussian operations
- URL: http://arxiv.org/abs/2110.08075v2
- Date: Wed, 26 Jan 2022 07:07:49 GMT
- Title: Conversion of Gaussian states under incoherent Gaussian operations
- Authors: Shuanping Du, Zhaofang Bai
- Abstract summary: We study when can one coherent state be converted into another under incoherent operations.
The structure of incoherent Gaussian operations of two-mode continuous-variable systems is discussed further.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The coherence resource theory needs to study the operational value and
efficiency which can be broadly formulated as the question: when can one
coherent state be converted into another under incoherent operations. We answer
this question completely for one-mode continuous-variable systems by
characterizing conversion of coherent Gaussian states under incoherent Gaussian
operations in terms of their first and second moments. The no-go theorem of
purification of coherent Gaussian states is also built. The structure of
incoherent Gaussian operations of two-mode continuous-variable systems is
discussed further and is applied to coherent conversion for pure Gaussian
states with standard second moments. The standard second moments are images of
all second moments under local linear unitary Bogoliubov operations. As
concrete applications, we obtain some peculiarities of a Gaussian system: (1)
There does not exist a maximally coherent Gaussian state which can generate all
coherent Gaussian states; (2) The conversion between pure Gaussian states is
reversible; (3) The coherence of input pure state and the coherence of output
pure state are equal.
Related papers
- Efficient conversion from fermionic Gaussian states to matrix product states [48.225436651971805]
We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states.
It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems.
The potential of our method is demonstrated by numerical calculations in two chiral spin liquids.
arXiv Detail & Related papers (2024-08-02T10:15:26Z) - On the equivalence between squeezing and entanglement potential for
two-mode Gaussian states [6.152099987181264]
The maximum amount of entanglement achievable under passive transformations by continuous-variable states is called the entanglement potential.
Recent work has demonstrated that the entanglement potential is upper-bounded by a simple function of the squeezing of formation.
We introduce a larger class of states that we prove saturates the bound, and we conjecture that all two-mode Gaussian states can be passively transformed into this class.
arXiv Detail & Related papers (2023-07-19T18:00:23Z) - Quantum Maximal Correlation for Gaussian States [2.9443230571766845]
We compute the quantum maximal correlation for bipartite Gaussian states of continuous-variable systems.
We show that the required optimization for computing the quantum maximal correlation of Gaussian states can be restricted to local operators that are linear in terms of phase-space quadrature operators.
arXiv Detail & Related papers (2023-03-13T14:29:03Z) - Matched entanglement witness criteria for continuous variables [11.480994804659908]
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states.
This opens a way for precise detection of non-Gaussian entanglement.
arXiv Detail & Related papers (2022-08-26T03:45:00Z) - Incoherent Gaussian equivalence of $m-$mode Gaussian states [0.0]
We show that two Gaussian states are incoherent equivalence if and only if they are related by incoherent unitaries.
Incoherent equivalence of Gaussian states is equivalent to frozen coherence.
arXiv Detail & Related papers (2022-06-26T09:31:57Z) - Deterministic Gaussian conversion protocols for non-Gaussian single-mode
resources [58.720142291102135]
We show that cat and binomial states are approximately equivalent for finite energy, while this equivalence was previously known only in the infinite-energy limit.
We also consider the generation of cat states from photon-added and photon-subtracted squeezed states, improving over known schemes by introducing additional squeezing operations.
arXiv Detail & Related papers (2022-04-07T11:49:54Z) - Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian
circuits [68.8204255655161]
We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements.
For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems can be employed to assess the simulatability.
arXiv Detail & Related papers (2022-03-21T17:57:02Z) - The Connection between Discrete- and Continuous-Time Descriptions of
Gaussian Continuous Processes [60.35125735474386]
We show that discretizations yielding consistent estimators have the property of invariance under coarse-graining'
This result explains why combining differencing schemes for derivatives reconstruction and local-in-time inference approaches does not work for time series analysis of second or higher order differential equations.
arXiv Detail & Related papers (2021-01-16T17:11:02Z) - Local optimization on pure Gaussian state manifolds [63.76263875368856]
We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm.
The method is based on notions of descent gradient attuned to the local geometry.
We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
arXiv Detail & Related papers (2020-09-24T18:00:36Z) - Gaussian conversion protocols for cubic phase state generation [104.23865519192793]
Universal quantum computing with continuous variables requires non-Gaussian resources.
The cubic phase state is a non-Gaussian state whose experimental implementation has so far remained elusive.
We introduce two protocols that allow for the conversion of a non-Gaussian state to a cubic phase state.
arXiv Detail & Related papers (2020-07-07T09:19:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.