- Bound-entanglement, or non-distillable entanglement, is not a rare phenomenon for continuous variable Gaussian states.
- The document presents a class of Gaussian states for a 2+2 mode bipartite system that are provably positive partial transpose (PPT) entangled within a finite parameter range, demonstrating bound-entanglement is achievable.
- This PPT entangled Gaussian state can be experimentally realized using current linear optics and squeezing techniques, challenging the notion that bound-entanglement is inaccessible in practice for continuous variable systems.
Dealing with Notations and conventions in tensor analysis-Einstein's summation convention covariant and contravariant and mixed tensors-algebraic operations in tensor symmetric and skew symmetric tensors-tensor calculus-Christoffel symbols-kinematics in Riemann space-Riemann-Christoffel tensor.
Devaney Chaos Induced by Turbulent and Erratic FunctionsIOSRJM
Let I be a compact interval and f be a continuous function defined from I to I. We study the relationship between tubulent function, erratic function and Devaney Chaos.
Dealing with Notations and conventions in tensor analysis-Einstein's summation convention covariant and contravariant and mixed tensors-algebraic operations in tensor symmetric and skew symmetric tensors-tensor calculus-Christoffel symbols-kinematics in Riemann space-Riemann-Christoffel tensor.
Devaney Chaos Induced by Turbulent and Erratic FunctionsIOSRJM
Let I be a compact interval and f be a continuous function defined from I to I. We study the relationship between tubulent function, erratic function and Devaney Chaos.
Contact geometry is the study of certain geometric structures on odd dimensional smooth manifolds. A contact structure is a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a Hamiltonian-like vector field called the Reeb vector field on the manifold. I will give some background on this subject, including motivation from classical mechanics. I will also explain how to make use of J-holomorphic curves to obtain a Floer theoretic contact invariant, contact homology, whose chain complex is generated by closed Reeb orbits. This talk will feature numerous graphics to acclimate people to the realm of contact geometry.
Maxwell's formulation - differential forms on euclidean spacegreentask
One of the greatest advances in theoretical physics of the nineteenth
century was Maxwell’s formulation of the the equations of electromag-
netism. This article uses differential forms to solve a problem related
to Maxwell’s formulation. The notion of differential form encompasses
such ideas as elements of surface area and volume elements, the work
exerted by a force, the flow of a fluid, and the curvature of a surface,
space or hyperspace. An important operation on differential forms is
exterior differentiation, which generalizes the operators div, grad, curl
of vector calculus. the study of differential forms, which was initiated
by E.Cartan in the years around 1900, is often termed the exterior
differential calculus.However, Maxwells equations have many very im-
portant implications in the life of a modern person, so much so that
people use devices that function off the principles in Maxwells equa-
tions every day without even knowing it
Published by:
Wang Jing
School of Physical and Mathematical Sciences
Nanyang Technological University
jwang14@e.ntu.edu.sg
Methods to determine pressure drop in an evaporator or a condenserTony Yen
This articles aims to explain how one can relatively easily calculate the pressure drop within a condenser or an evaporator, where two-phase flow occurs and the Navier-Stokes equation becomes very tedious.
Contact geometry is the study of certain geometric structures on odd dimensional smooth manifolds. A contact structure is a hyperplane field specified by a one form which satisfies a maximum nondegeneracy condition called complete non-integrability. The associated one form is called a contact form and uniquely determines a Hamiltonian-like vector field called the Reeb vector field on the manifold. I will give some background on this subject, including motivation from classical mechanics. I will also explain how to make use of J-holomorphic curves to obtain a Floer theoretic contact invariant, contact homology, whose chain complex is generated by closed Reeb orbits. This talk will feature numerous graphics to acclimate people to the realm of contact geometry.
Maxwell's formulation - differential forms on euclidean spacegreentask
One of the greatest advances in theoretical physics of the nineteenth
century was Maxwell’s formulation of the the equations of electromag-
netism. This article uses differential forms to solve a problem related
to Maxwell’s formulation. The notion of differential form encompasses
such ideas as elements of surface area and volume elements, the work
exerted by a force, the flow of a fluid, and the curvature of a surface,
space or hyperspace. An important operation on differential forms is
exterior differentiation, which generalizes the operators div, grad, curl
of vector calculus. the study of differential forms, which was initiated
by E.Cartan in the years around 1900, is often termed the exterior
differential calculus.However, Maxwells equations have many very im-
portant implications in the life of a modern person, so much so that
people use devices that function off the principles in Maxwells equa-
tions every day without even knowing it
Published by:
Wang Jing
School of Physical and Mathematical Sciences
Nanyang Technological University
jwang14@e.ntu.edu.sg
Methods to determine pressure drop in an evaporator or a condenserTony Yen
This articles aims to explain how one can relatively easily calculate the pressure drop within a condenser or an evaporator, where two-phase flow occurs and the Navier-Stokes equation becomes very tedious.
Integrability and weak diffraction in a two-particle Bose-Hubbard model jiang-min zhang
We report a bound state, which is embedded in the continuum spectrum, of the one-dimensional two-particle (Bose or Fermion) Hubbard model with an impurity potential. The state has the Bethe-ansatz form, although this model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.
To make Reinforcement Learning Algorithms work in the real-world, one has to get around (what Sutton calls) the "deadly triad": the combination of bootstrapping, function approximation and off-policy evaluation. The first step here is to understand Value Function Vector Space/Geometry and then make one's way into Gradient TD Algorithms (a big breakthrough to overcome the "deadly triad").
Basic concepts and how to measure price volatility
Presented by Carlos Martins-Filho at the AGRODEP Workshop on Analytical Tools for Food Prices
and Price Volatility
June 6-7, 2011 • Dakar, Senegal
For more information on the workshop or to see the latest version of this presentation visit: http://www.agrodep.org/first-annual-workshop
I am George P. I am a Stochastic Processes Assignment Expert at statisticsassignmenthelp.com. I hold a Master's in Statistics, Malacca, Malaysia. I have been helping students with their homework for the past 8 years. I solve assignments related to Stochastic Processes.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Stochastic Processes Assignments.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
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Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
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UI automation Sample
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Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
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LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
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Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
How world-class product teams are winning in the AI era by CEO and Founder, P...
Bound entanglement is not rare
1. Bound-entanglement is NOT a rare phenomenon for
continuous variable Gaussian states
R. Simon
The Institute of Mathematical Sciences, Chennai.
January 07, 2013
2. Convex Subsets of state space
A bipartite state ρAB is separable iff it CAN BE written in the form
ρAB =
j
pj ρAj ⊗ ρBj , pj > 0.
A non-separable (entangled) state may or may not be distillable
All PPT states are provably non-distillable.
But it is not known if all NPT states are distillable.
Non-distillable entanglement is called bound entanglement
Ωsep ⊂ ΩPPT ⊆ ΩND ⊂ Ω.
Like the full state space Ω, all these subsets are CONVEX.
3. Nowhere dense: measure zero
Horodecki, Cirac, Lewenstein (2001)
“Bound entanglement for continuous variables is a rare phenomenon”
proved that ΩND is nowhere dense in Ω, IN THE CASE of continuous
variable systems (infinite-dimensional Hilbert spaces)
Implies that ΩPPT is nowhere dense in Ω, and so also is Ωsep.
This important negative result would seem to be a no-go-theorem for
experimentalists.
Any attempt to produce a state in ΩND would land outside of ΩND,
with probability one (i.e. almost certainly).
Should experimentalists take this result as a no-go-theorem?
The rest of the talk will examine this issue in the case of Gaussians.
4. Gaussian states
Gaussian states are those whose quasi-probability has Gaussian form.
P, W , Q are the more popular quasi-probabilities.
If one of them is Gaussian, so are the others. We use W.
Phase-space displacements do not affect our considerations
⇒ WLOG we may assume the state to be a zero-mean state :
ξ = 0, ξ = (q1, p1; q2, p2; · · · , qn, pn).
Then the quasi-probability (state) is fully determined
by the variance matrix V :
Vαβ =
1
2
{ξα, ξβ}, α, β = 1, 2, · · · , 2n;
W (ξ) = A exp[−ξT
V −1
ξ].
A ensures W (ξ)d2nξ = 1 ⇔ trρ = 1.
ρ ≥ 0 ⇔ V +iΛ ≥ 0 (uncertainty principle), Λ = iσ2 ⊕iσ2 ⊕· · ·⊕iσ2.
5. Canonical transformations : Uncertainty Principle
Linear canonical transformations S ∈ Sp(2n, R), i.e. SΛST = Λ,
act unitarily on the Hilbert space through U(S)
S → U(S) : |ψ → U(S)|ψ , ρ → U(S) ρ U(S)†
.
The induced action on the quasi-probability is
U(S) : W (ξ) → W
′
(ξ) = W (S−1
ξ), V → V
′
= SVST
.
The Uncertainty Principle V + iΛ ≥ 0 ⇔ V ≥ ΛV −1ΛT
⇔ V ≥ SST
, for some S ∈ Sp(2n, R)
Every V > 0 is necessarily of the form
V = SV0ST
, S ∈ Sp(2n, R), V0 = diag (κ1, κ1; κ2, κ2; · · · ; κn, κn)
V + iΛ ≥ 0 ⇔ κ1 ≥ κ2 ≥ · · · ≥ κn ≥ 1.
6. PPT entangled Gaussians
Bipartite system of k + ℓ = n modes, k with Alice, ℓ with Bob.
Λ = ΛA ⊕ ΛB
ΛA = iσ2 ⊕ iσ2 ⊕ · · · ⊕ iσ2, (2k dimensional)
ΛB = iσ2 ⊕ iσ2 ⊕ · · · ⊕ iσ2, (2ℓ dimensional)
V + iΛ ≥ 0 ⇔ V − iΛ ≥ 0 (transpose or time-reversal).
Separable V necessarily obeys
V + iΛPT
≥ 0, ΛPT
= ΛA ⊕ (−ΛB) (PPT criterion)
V ≥ SAST
A ⊕ SBST
B is a necessary and sufficient condition for
separability of Gaussian states, irrespective of k, ℓ
In the special case of k = 1 (or ℓ = 1), the two criteria are equivalent,
and the PPT criterion becomes NS.
i.e., PPT entangled Gaussians can occur only when BOTH k, ℓ ≥ 2.
7. A class of PPT variance matrices : Uncertainty Principle
First example of a PPT entangled Gaussian state : Werner and Wolf
(2001)
Consider the 2 + 2-mode Gaussians defined by
V =
a cR
cRT a
, a > 1, c real,
R =
1 0 0 0
0 0 0 −1
0 0 −1 0
0 −1 0 0
= RT
= R−1
.
trR = 0, R2 = 11 ⇒ doubly degenerate eigenvalues ±1.
UP : V ≥ ΛV −1
ΛT
⇔ |c| ≤ a2 − 2a2 − 1
⇒ V is an acceptable variance matrix iff c2 ≤ a2 −
√
2a2 − 1.
8. Effect of Partial Transpose
Under partial transpose :
R =
1 0 0 0
0 0 0 −1
0 0 −1 0
0 −1 0 0
→
1 0 0 0
0 0 0 1
0 0 −1 0
0 1 0 0
= SA
0 R(SB
0 )T
,
where SA
0 = SB
0 = diag(−1, −1, 1, 1).
Thus, partial transposition on V corresponds to V → S0VST
0 , where
S0 = diag (−1, −1, 1, 1, −1, −1, 1, 1).
⇒ PT of V0 is UNITARILY EQUIVALENT to V .
⇒ The Gaussian state V is PPT, for all (a, c).
9. Separability
Since the state is essentially invariant under PT, the partial transpose
criterion is of no use. So we resort to the stronger NS criterion
V ≥ SAST
A ⊕ SBST
B .
Consider the four dimensional projection
Ω =
1 −RT
−R 1
.
For separable V , one necessarily has
tr(VΩ) ≥ trSAST
A + trSBST
B ≥ 8.
For our V we have tr(VΩ) = 8(a − c)
⇒ a − 1 ≥ |c| is a NECESSARY condition for separability.
Since this implies V ≥ 1, and since 1 is of the form SAST
A + SBST
B ,
the condition a − 1 ≥ |c| is SUFFICIENT as well.
10. Recapitulation
Since V is invariant under PT, it can never be NPT entangled.
Positivity of ρ ⇔ c2 ≤ a2 −
√
2a2 − 1, Separability of ρ ⇔ a − |c| ≥ 1
With a = 2 : ρ is a state if |c| ≤ 4 −
√
7 = 1.164. And ρ is
separable iff |c| ≤ 1. If |c| > 1.164, then ρ is not even a state!
There is a FINITE parameter range
a − 1 < |c| ≤ a2 − 2a2 − 1 which is 1 < |c| ≤ 1.164 for a = 2.
in which the state is PPT entangled.
With a = 2, c0 = 1.08 is ‘deep’ in the interior of the PPT entangled
region of extent △c = 0.164.
11. NOT a rare phenomenon
When the uncertainty inequality |c| ≤ a2 −
√
2a2 − 1 is saturated, two
of the invariant κ’s equal unity, and the other two equal a2 − c2. Let V0
correspond to (a, c0) in the ‘deep’ interior.
Then, every κ ≥ 1 + ǫ for some ǫ > 0. And tr(ΩV0) = 8(1 − 0.08).
With Γ real symmetric and trΓ2 ≤ 1, V0 + rΓ corresponds to
a solid ball of radius r in Rn(2n+1) [n = 4 for us] around V0;
Choose r << ǫ
The entire ball V0 + rΓ comprises bonafide variance matrices
trΩ(V0 + rΓ) < 8 for the entire ball hence all states non-separable
Since the ball itself is PT symmetric, it has no NPT entangled state.
12. Laboratory Feasibility
At the minumum : We have shown that inseparable PPT variance
matrix is not a rare phenomenon.
Restricted to Gaussian states of the state space, this implies
PPT-entangled Gaussian state is not a rare phenomenon.
The considered state can be produced using linear optics and a pair of
inseparable two-mode Gaussian states.
Arbitrarily small squeezing is sufficient and, in particular, currently
available levels of squeezing suffice.
It is true that there could be non-Gaussian states arbitrarily close to
the considered Gaussian state.
Any number of papers talk about separable Gaussian states and
entanglement death. No need to be more apologetic!
Finally, there are physical processes whose output is guaranteed to be
Gaussian states.