Quantum Information Viewed by a Theoretical Physicist Lajos Di osi - - PowerPoint PPT Presentation

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Quantum Information Viewed by a Theoretical Physicist Lajos Di osi - - PowerPoint PPT Presentation

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Quantum Information Viewed by a Theoretical Physicist Lajos Di osi Wigner Center, Budapest 2012. december 2. Acknowledgements go to: Hungarian Scientific Research Fund under Grant No. 75129 EU COST Action MP1006 Fundamental Problems in

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SLIDE 1

Quantum Information Viewed by a Theoretical Physicist

Lajos Di´

  • si

Wigner Center, Budapest

  • 2012. december 2.

Acknowledgements go to: Hungarian Scientific Research Fund under Grant No. 75129 EU COST Action MP1006 ‘Fundamental Problems in Quantum Physics’

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

1 / 15

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SLIDE 2

1

Frontlines of Quantum Theory 1900-2000-...

2

When I Started my Studies ...

3

No-cloning, Linearity

4

Peres-Horodecki Entanglement Criterion

5

Factorization vs Period Finding

6

Quantum Circuit Language

7

Summary

8

Who Eliminates the Schr¨

  • dinger Cat?

9

Monitoring the Cat: Nano-Quantum-Mechanical Experiments

10 DP and Beyond DP

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

2 / 15

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SLIDE 3

Frontlines of Quantum Theory 1900-2000-...

Frontlines of Quantum Theory 1900-2000-...

black-body radiation atoms, molecules electron condensed matter electrodynamics nuclei elementary particles gravitation ? cosmology ? information living material? brain, consciousness?

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

3 / 15

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When I Started my Studies ...

When I Started my Studies ...

Quantumness meant quantizedness (discrete energies, gaps, etc. State vector Ψ was extensively and exclusively used, density matrix ˆ ρ was only taught for spins and Gibbs-ensembles. Shannon information theory gained limited interest in physics. Single system quantum mechanics was taught, but was not testable. Today Quantumness means entanglement, quantum enhancement in informatics, computation, metrology, etc. Density matrix ˆ ρ is recognized and taught as the generic representative of quantum state. Quantum information is exciting physics. So Shannon is taught. Single system quantum mechanics is directly testable.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

4 / 15

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SLIDE 5

No-cloning, Linearity

No-cloning, Linearity

Wootters and Zurek (1982): Cloning a single unknown qubit, ˆ ρ − → ˆ ρ ⊗ ˆ ρ is impossible. Believed to guarantee quantum security protocols. Gisin (1990): Any non-linear modification of QM, ˆ ρ − → Nonlin(ˆ ρ) leads to FTL signalling. Believed to be an exciting quantum paradox. Wisdom 10-20 yy later: the same things hold classically!

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

5 / 15

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No-cloning, Linearity

Everyday wisdom in classical statistics x − → CLASSICAL BLACK BOX MACHINE − → y The distribution ρ′(y) is a linear map of ρ(x). Nobody would challenge linearity. Cloning, ρ(x) → ρ(x)ρ(x) is

  • forbidden. FTL would be derived if anyone challenged linearity.

No everyday wisdom in quantum statistics. Therefore ... ... sometimes we are challenging the linearity of ˆ x − → QUANTUM BLACK BOX MACHINE − → ˆ y Non-linearity contradicts to the statistical interpretation of ˆ ρ. The linearity of quantum operations ˆ ρ − → Mˆ ρ is rooted deeper than we thought before.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

6 / 15

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SLIDE 7

Peres-Horodecki Entanglement Criterion

Peres-Horodecki Entanglement Criterion

Werner (1989): Mixed state is separable (unentangled) iff: ˆ ρAB =

  • wλˆ

ρλ

A ⊗ ˆ

ρλ

B

No easy-to-apply analytic separability test until Peres observation (1995): Partial transpose (I ⊗ T )ˆ ρAB =

  • wλˆ

ρλ

A ⊗ T ˆ

ρλ

B

  • f separable state is a legal density matrix while this is not true for

non-separable states. Peres-Horodecki (1995): A two-qubit bipartite ˆ ρAB is separable iff its partial transpose is non-negative.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

7 / 15

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Peres-Horodecki Entanglement Criterion

Peres-Horodecki Entanglement Criterion

Separability: physical feature; transpose ˆ ρ → T ˆ ρ is a math option. We need the physical meaning for T ! Wigner (1931): Time-reversal operator is anti-unitary. T is equivalent with time-reversal operation. Peres-Horodecki criterion, for theoretical physicist: Two-qubit ˆ ρAB is separable iff its partial time-reversal is non-negative. Partial time-reversal of a two-qubit entangled state is not a state. Exciting physical implication: Reversal of local time arrow ↑ in region A ↓ in region B is possible in classical cosmology. It is forbidden in QM.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

8 / 15

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SLIDE 9

Factorization vs Period Finding

Factorization vs Period Finding

Feynman (1982): Exponential slowdown of classical simulation Shor quantum algorithm (1994): Exponential speedup of number factorization Breaking RSA (1976) cryptography becomes possible. Theoretical physicist insight is different. Exponential speedup of what? Factorization = Period Finding (plus a few boring algebraic steps) Shor quantum algorithm for theoretical physicist: Exponential speedup of period finding. Exponential speedup of pattern recognition. Toward understanding animal, human intellect.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist

  • 2012. december 2.

9 / 15

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Quantum Circuit Language

Quantum Circuit language

von Neumann detector (1932) System Ψ(x), x =?. Detector φ(y) is peaked around y = 0. Coupling HI = δ(t)x(i∂/∂y). Ψ(x)φ(y) = ⇒ Ψ(x)φ(y + x) φ becomes peaked around x. von Neumann detector (2000-...)

x x y=0 x

.

Discretized scheme of time-continuous detection (monitoring):

....

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 10 / 15

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Summary

Summary

black-body radiation atoms, molecules electron condensed matter electrodynamics nuclei elementary particles gravitation ? cosmology ? information living material? brain,consciousness? Quantum information has changed and reformed our understanding quantum mechanics. It sharpened and deepened our insight into the foundations (I gave very occasio- nal and unfairly personal examp- les). The fruitful and fertilizing impact of quantum information on physics, on learning and teach- ing quantum mechanics will surely continue in the coming years. Keep eyes open: in qubit there can be more physics than information.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 11 / 15

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SLIDE 12

Who Eliminates the Schr¨

  • dinger Cat?

Who Eliminates the Schr¨

  • dinger Cat?

Mechanical Schr¨

  • dinger Cat
  • D. (1987), Penrose (1996):

Hypothetic, gravity-related decoherence/collapse. Strength heavily depends on mass resolution: collapse takes hours or milliseconds.

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 12 / 15

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SLIDE 13

Who Eliminates the Schr¨

  • dinger Cat?

Optomechanics, state of art June 2012

Quantum-Coherent Coupling of a Mechanical Oscillator to an Optical Cavity Mode

Ewold Verhagen, Samuel Deleglise, Albert Schliesser, Stefan Weis, Vivishek Sudhir, Tobias J. Kippenberg

Laboratory of Photonics and Quantum Measurements, EPFL Part time affiliation: Max Planck Institute of Quantum Optics 19th June 2012

  • Collaborators

EPFL-CMI K. Lister (EPFL)

  • J. P. Kotthaus (LMU)
  • W. Zwerger (TUM)
  • I. Wilson-Rae (TUM)

A. Marx (WMI)

  • J. Raedler (LMU)
  • R. Holtzwarth (MenloSystem)
  • T. W. Haensch (MPQ)

Marie Curie ITN

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 13 / 15

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SLIDE 14

Monitoring the Cat: Nano-Quantum-Mechanical Experiments

Monitoring the Cat: Nano-Quantum-Mechanical Experiments

Vibrating micro-mirror (Leiden) Levitating micro-dielectrics (Vienna-Garching) ... on space satellite (Vienna-Garching-Pasadena) Silica micro-resonator (Garching-Pasadena)

Aspelmeyer et al.: Quantum Optomechnanics - Throwing a Glance, J.Opt.Soc.Am. B27, A189 (2010)

Currently: 10−12g-1g, kHz-GHz, mK — but µK needed!

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 14 / 15

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SLIDE 15

DP and Beyond DP

DP and Beyond DP

ρ Newton oscillator ~ 1012g/cm3 ωG ωG

nucl

Newton field of a moving He tank would be delayed by about 1h. Consequence: Newton field of a moving condensed source is delayed by ms’s. = √Gρnucl ~ 102/s ωG

nucl

G Gρ ~ 10−4 /s ω = √ period ~1h period ~1ms ρnucl ρ ~ 1g/cm3 G−related (DP) model predicts collapse rate in condensed matter in He superfluid 1) Newton gravity is caused by DP−collapse. Proposal beyond DP−model: 2) Gravity’s emergence rate is the collapse rate. Next: What components (short/long range) are delayed? Minimum model of emergence is needed for the experimental proposal. Theoretical stress: violation of equivilance principle, momentum conservation, etc. * * *

Lajos Di´

  • si (Wigner Center, Budapest)

Quantum Information Viewed by a Theoretical Physicist 2012. december 2. 15 / 15