cvteleportationfinal

8/4/2019 cvteleportationfinal

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(a) Paranormal phenomena

(b) Men are from Mars. Women are from Venus

(c) Physics


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Classical phase-space descriptions ofcontinuous-variable teleportation

Carlton M. Caves and Krzysztof WodkiewiczPRL 69, 040506 (2004), quant-ph/0401149)

UNM Information Physics

info.phys.unm.edu

Teleportation fidelity andsub-Planck phase-space structure

Carlton M. Caves and Andrew J. Scottin preparation

Fidelity of Gaussian channels

Carlton M. Caves and Krzysztof WodkiewiczFidelity of Gaussian channels, Open Syst & Inf Dynamics 11, 309 (2004)


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This photo shows JeremyCaves walking faster than

the shutter speedsomewhere in Australia.

Where is it?


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This photo shows ascene somewhere in New

Mexico.

Where is it?


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Continuous-variable teleportation

Furasawa et al., Science 282, 706 (1998)Teleportation ofcoherent states

Bowen et al., PRA 67, 032302 (2003)

Zhang et al., PRA 67, 033792 (2003)


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Alice Bob

Gibberish

Two units of noise

Uncertainty-principle limits on simultaneous measurements of xand prequire


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Whoa! This is a classicalphase-space description

(local hidden-variable model)

Measure Communicate

Displace

No cloning

Gibberish


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Wigner function: A phase-space quasidistribution

Zureks compass state: Superposition of four coherent states

Marginals of the Wigner function give the statistics of measurements of thephase-space variables, xor p, or any linear combination of xand p.


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Wigner function: A phase-space quasidistribution

Marginals of the Wigner function give the statistics of measurements of thephase-space variables, xor p, or any linear combination of xand p.

Random superposition of first 100 number states


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Compass state: Superposition of four coherent states

MeasureMeasure

Sub-Planck structure


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Sub-Planck structure


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Continuous-variable teleportation: Wigner functions

Measure

Communicate

Displace


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For Gaussian input states (this includes coherent states), all of which havepositive Wigner functions, the Wigner function provides a classical phase-space description (local hidden-variable model). The hidden variables arethe phase-space variables for the three modes. The protocol runs on theclassical correlations between the phase-space variables, described by theWigner function.


Yet if Alice and Bob share an unentangled state in modes A and B, themaximum fidelity for teleporting a coherent state using the standardprotocol is 1/2. For teleporting coherent states, a fidelity greater than 1/2requires a shared resource that quantum mechanics says is entangled, but

which is used in a way that can be accounted for by classical correlationsof local hidden variables.


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Measure

Communicate

Displace


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Continuous-variable teleportation: Input and entanglement

Squeeze parameter rMeasure of EPR correlations


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Continuous-variable teleportation: Output and fidelity


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Teleportation fidelity and sub-Planck structure


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Teleportation fidelity and sub-Planck structure

Our measure of small-scale phase-structure

finds an operational significance in terms ofthe difficulty of teleportation.


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Teleportation of non-Gaussian pure statesAllnon-Gaussian purestates have Wigner functions thattake on negative values, so they cannot be incorporatedin the classical phase-space description.

Kicking and cheating protocol

Alice kicksthe input state randomly with a Gaussian kicking strength tchosen so that the kicked state has a positive Wigner function and thus canbe incorporated within the classical phase-space description. The minimum

required kicking strength is t =1 for all non-Gaussian pure states.

Alice and Bob cheatby teleporting the kicked state with perfect fidelity.

The fidelity achieved by the kicking and cheating protocol is the t =1 fidelitywithin the standard quantum protocol.

Gold standard for continuousvariable teleportation ofnon-Gaussian pure states

?


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?

This same technical result shows that if Alice and Bob sharean unentangled state, the maximum fidelity for teleporting a

coherent state using the standard protocol is 1/2.

Turn the overlap question for

one mode into an expectationvalue for a pair of modes.


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The kicking with added communication protocol

Alice communicates her actual kick to Bob, who removes it aftercompleting the protocol, thereby achieving the quantum fidelity atthe cost of additional classical communication from Alice to Bob.


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There is a classical phase-space description (local hidden-variablemodel) for teleportation, with arbitrary fidelity, of all Gaussianpure states, including coherent states, using the standard protocol.

There is no classical phase-space description of the teleportation ofany non-Gaussian pure state for fidelities greater than or equal to

2/3, even if one allows Alice and Bob to cheat by using a protocolwith perfect fidelity.

If Alice and Bob share an unentangled state, they cannot teleport acoherent state using the standard protocol with fidelity greaterthan 1/2. For teleporting coherent states, a fidelity greater than1/2 requires a shared resource that quantum mechanics says is

entangled, but which is used in a way that can be accounted for byclassical correlations of local hidden variables.

Alice and Bob can achieve the quantum fidelity within a kicking withadded communication protocol in which Alice communicates the kick,

at the cost of upping the classical communication rate by 50%.

Summary


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Echidna GorgeBungle Bungle Range

Purnululu NP

Western Australia

2004 June 28

This photo shows Jeremy

Caves walking faster thanthe shutter speed

somewhere in Australia.

Where is it?


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This photo shows a

scene somewhere in NewMexico.

Where is it?

Sawtooth RangeWest of VLA

2003 August 31

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