steering witnesses and criteria for the non existence of local hidden state lhs models n.
Download
Skip this Video
Download Presentation
Steering witnesses and criteria for the (non-)existence of local hidden state (LHS) models

Loading in 2 Seconds...

play fullscreen
1 / 21

Steering witnesses and criteria for the (non-)existence of local hidden state (LHS) models - PowerPoint PPT Presentation


  • 71 Views
  • Uploaded on

Steering witnesses and criteria for the (non-)existence of local hidden state (LHS) models. Eric Cavalcanti, Steve Jones , Howard Wiseman Centre for Quantum Dynamics, Griffith University. Steve Jones, PIAF, 2 February ‘08. Interesting questions that I don’t plan to address….

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Steering witnesses and criteria for the (non-)existence of local hidden state (LHS) models' - cady


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
steering witnesses and criteria for the non existence of local hidden state lhs models

Steering witnesses and criteria for the (non-)existence of local hidden state (LHS) models

Eric Cavalcanti, Steve Jones, Howard Wiseman

Centre for Quantum Dynamics, Griffith University

Steve Jones, PIAF, 2 February ‘08

interesting questions that i don t plan to address
Interesting questions that I don’t plan to address…
  • Is steering an argument for the epistemic view of quantum states?
  • But isn’t that what Schrodinger meant…?
  • Do you consider contextuality for any of

this?

Steve Jones, PIAF, 2 February '08

outline or what i actually will talk about
Outline (or what I actually will talk about)
  • History and definitions
  • Steering criteria vs Steerability witnesses
    • (and Bell inequalities vs Bell-nonlocality witnesses)
  • Loopholes
  • Example
  • Open problems

Steve Jones, PIAF, 2 February '08

slide4

The Einstein-Podolsky-Rosen paradox (1935)

EPR’s assumptions:

  • Completeness:

“Every element of the physical reality must have a counterpart in the physical theory”.

  • Reality:

Accurate prediction ofa physical quantity → element of reality associated to it.

  • Local Causality:

No action at a distance

They considered a nonfactorizable state of the form:

Steve Jones, PIAF, 2 February '08

the einstein podolsky rosen paradox 1935
The Einstein-Podolsky-Rosen paradox (1935)

Alice

Bob

XA, PA

XB, PB

Quantum Mechanics predicts, for certain entangled states, xA = xB and pA = - pB; by measuring at A one can predict with certainty either xBor pB .

Therefore, elements of reality must exist for both xBand pB , but QM doesn’t predict these simultaneously.

  • EPR conclude that Quantum Mechanics is incomplete.

Steve Jones, PIAF, 2 February '08

schrodinger s 1935 response to epr
Schrodinger’s 1935 response to EPR
  • Schrodinger introduced the terms “entangled” and “steering” to describe the state and situation introduced by EPR.

“By the interaction the two representatives (or -functions) have become entangled.”

“What constitutes the entanglement is that is not a product of a function for x and a function for y.”

Steve Jones, PIAF, 2 February '08

slide7

Schrodinger’s 1935 response to EPR

  • Schrodinger emphasized that in the EPR paradox, and steering in general, the choice of measurement at one side is important.
  • Alice can steer Bob’s state if she can prepare different ensembles of states for Bob by performing (at least 2) different measurements on her system.

Steve Jones, PIAF, 2 February '08

what about mixed states
What about mixed states?
  • Both EPR and Schrodinger considered pure states in their 1935 works.
  • For pure states: entangled = steerable (=Bell nonlocal)
  • Even with improvements in modern experiments we must deal with states which are mixed.
  • How does all this generalize?
  • EPR paradox EPR-Reid criteria
  • Schrodinger steeringPRL 98, 140402 (2007)

Steve Jones, PIAF, 2 February '08

mathematical definitions
Mathematical definitions

Separable: A local hidden state (LHS) model for both parties

Non-steerable: A local hidden state (LHS) model for one party

Bell local: A local hidden variable (LHV) model for both parties

Steve Jones, PIAF, 2 February '08

why experimental steering criteria
Why experimental steering criteria?
  • Foundational arguments aside for a moment.
  • Demonstration of the EPR effect: local causality is false or Bob’s system cannot be quantum (quantum mechanics is incomplete)
  • Easier to get around detection loophole than Bell’s
  • Hopefully applications in quantum information processing tasks?

Steve Jones, PIAF, 2 February '08

two types of problems
Two types of problems
  • Experimental steering:
    • Given sets of measurements for Alice and Bob and a preparation procedure, can the experimental outcomes associated with this setup demonstrate steering?

That is, do they violate the assumption of a local hidden state model for Bob?

    • Definition:

Any sufficient criterion for experimental steering will be called a steering criterion.

Steve Jones, PIAF, 2 February '08

two types of problems1
Two types of problems
  • State steerability:
    • Given a quantum state, can it demonstrate steering with some measurements for Alice and Bob?
    • Definition:

Any sufficient criterion for state steerability will be called a steerability witness.

Steve Jones, PIAF, 2 February '08

review linear entanglement witnesses
Review: (linear) Entanglement witnesses
  • Reasoning: There exists a plane separating a convex set (separable states) and a point outside of it (the entangled state).
  • The same is true for any convex set (e.g. non-steerable states).

Steve Jones, PIAF, 2 February '08

steerability witnesses
Steerability Witnesses

Lemma: A bipartite density matrix on is steerable if and only if there exists a Hermitian operator such that

and for all non-steerable density matrices .

However, the measurements required to determine do not necessarily violate a LHS model.

Compare with Bell-nonlocality witnesses vs Bell inequalities

Steve Jones, PIAF, 2 February '08

witnesses and experimental criteria
Witnesses and experimental criteria
  • Witnesses: surfaces on the space of states;
  • Experimental criteria: surfaces on the space of correlations.

Steve Jones, PIAF, 2 February '08

experimental steering criteria
Experimental steering criteria
  • Bell inequalities are experimental criteria derived from LHV models.
    • Violation implies failure of LHV theories.
  • Analogously, experimental steering criteria are derived from the LHS model (for Bob).
    • Violation implies steering.

Steve Jones, PIAF, 2 February '08

loop holes
Loop-holes
  • All experimental tests of Bell inequalities have suffered from the detection and/or locality loop-hole.
  • How do loop-holes affect the experimental demonstration of steering?

Steve Jones, PIAF, 2 February '08

loop holes1
Loop-holes
  • Locality loop-hole:
    • Not obvious that this loop-hole would apply to a demonstration of steering.
    • Although, to be rigorous, one must assume that once Bob obtains his system, Alice cannot affect it (or the outcomes reported by Bob’s detectors).

Steve Jones, PIAF, 2 February '08

loop holes2
Loop-holes
  • Detection loop-hole:
    • Clearly this loop-hole will affect a demonstration of steering.
    • If Alice’s detectors are inefficient

→ harder for her to steer to a given ensemble.

    • As for Bell nonlocality, there will be a threshold detection efficiency that allows a loop-hole free demonstration.
    • The threshold efficiency for steering will be lower than for Bell nonlocality.

Steve Jones, PIAF, 2 February '08

steering criteria example
Steering criteria example
  • Consider the two-qubit Werner state
  • Assuming a LHS model for Bob, the following steering criteria must be satisfied:
  • For n=2, this inequality is violated for
  • For n=3, this drops to

Steve Jones, PIAF, 2 February '08

summary and open problems
Summary and open problems
  • LHS model is the correct formalisation of the concept of steering introduced by Schrodinger as a generalisation of the EPR paradox;
  • Steerability witnesses and steering criteria;
  • Is there a general algorithm to generate all steering criteria?
  • What is the set of steerable states?
    • e.g., are there asymmetric steerable states?
  • Can the concept of Bell-nonlocality witnesses help in studying the set of Bell-local states?
  • Applications of steering to quantum information processing tasks?
  • What features of toy models allow steering in general?

Steve Jones, PIAF, 2 February '08