Quantum info tools toys for quantum gravity Daniel
- Slides: 23
Quantum info tools & toys for quantum gravity Daniel Terno Perimeter Institute LOOPS `05
Outline MEASUREMENTS POVM Information gain DYNAMICS Completely positive maps Non completely positive maps ENTANGLEMENT Entang’t 101 BH applications
MEASUREMENTS POVM discrete continuous Projections/von Neumann Realization Moments ancillary system+ unitary evolution+ PVM
Construction: covariance considerations and /or optimization Use: decision/identification unsharp properties non-commuting variables/ phase space observables Coexistence & uncertainty
TETRAHEDRON Classical geometry • 6 edges • 3 edges, 3 angles • 3 edges, 3 products • 3 areas, 3 dihedral angles • 4 areas, 2 dihedral angles Volume
Quantum mechanics 5 commuting observables Basis: eigenvectors of Standard uncertainty relation
Question How uncertain is the shape and how this uncertainty decreases in the classical limit? Observation 1 [numeric] Observation 2 Naïve bound
More precise formulation: quantum communication problem 1. Fix the areas 2. Encode the angles 3. Decode 4. Calculate the figure of merit 5. Average over all angles 6. Take the limit
Priors At least two natural probability distributions or Fixing 4 areas
Encoding & distance Condition Figure of merit POVM Spin POVM
ILLUSTRATION (1, 1, 1, 1) tetrahedron Optimization: Constraint: Independent variables: phases
DYNAMICS Unitary Completely positive Definition: Physics: Def: unital map
Non completely positive Unitary evolution & partial trace Physically acessible
Causal sets Hawkins, Markopoulou, Sahlmann CQG 20, 3839 (2003) CNOT gate
Causal sets Partial sets: unital CP dynamics? Lemma: physically accessible and unital => CP
ENTANGLEMENT a brief history Ancient times: 1935 -1993 “The sole use of entanglement was to subtly humiliate the opponents of QM” Modern age: 1993 Resource of QIT Teleportation, quantum dense coding, quantum computation…. Postmodern age: 1986 (2001)Entanglement in physics
ENTANGLEMENT a closer encounter Pure states 1 0. 8 0. 6 0. 4 0. 2 0. 4 0. 6 Mixed states hierarchy Direct product Separable Entangled 0. 8 1
Entanglement of formation ENTANGLEMENT measures Minimal weighted average entanglement of constituents
Coincide on pure states with n w o n k Zero on unentangled states “Good” measures of entanglement: satisfy three axioms r e v e n t s o m Al Do not increase under LOCC
Entropy and entanglement on the horizon gr-qc/0508085 gr-qc/0505068 Phys. Rev. A 72 022307 (2005) Etera Livine, Tuesday I, 16: 00
Evaporation
Summary MEASUREMENTS POVM Information gain DYNAMICS Completely positive maps Non completely positive maps ENTANGLEMENT Entang’t 101 BH applications
Thanks to Hilary Carteret Viqar Husain Netanel Lindner Etera Livine Lee Smolin Oliver Winkler Karol Życzkowski
- Gravity for dummies and dummies for gravity equations
- Similar image search
- Loop quantum gravity
- Classical physics
- Quantum physics vs quantum mechanics
- Materi bahasa inggris kelas 6 tentang ownership
- Rawan plushie
- Nn toys
- Colonial games and toys
- Benny's educational toys
- Www.tasc-toys.com
- Toy mold making
- Wooden desk toys
- What does santa carry the toys in
- What do children hang up for santa to put the toys in?
- Types of mechanical toys
- Toys for tots st mary's county md
- Show me your toys
- Reggio emilia toys
- Best travel toys for toddlers
- Assistive technology toys
- The falsification principle
- Plural of library
- Lulu rocking horse