Non-Locality and Communication Complexity Stefan Wolf Università della Svizzera italiana Darmstadt,

Ferdinand Gonseth 1936 Logic and Physics La logique est tout d'abord une science naturelle.

Ernst Specker 1961 Is it possible to embed the description of any physical system into classical logic? Logic and Physics

For Qbits: YES Ernst Specker 1967 Simon Kochen

Ernst Specker 1967 Non-contextual deterministic preparation for all measurements: Output the vector closest to. Simon Kochen For Qbits: YES

Bell Inequality: Correlations from Shared Information John Bell 1964 John Bell

1964 Bell Inequality: Correlations from Shared Information

John Bell 1964 Bell Inequality: Correlations from Shared Information

John Bell 1964 Bell Inequality: Correlations from Shared Information

John Bell 1964 Bell Inequality: Correlations from Shared Information

... PR Sandu Popescu 1994 Daniel Rohrlich John Bell 1964 Bell Inequality: Correlations from Shared Information

Phenomena of Quantum Physics: Non-Locality John Bell 1964 Colored cards: 75% Photons:...

Phenomena of Quantum Physics: Non-Locality John Bell Colored cards: 75% Photons: ~85% ! Spontaneous correlations = ''Non-locality''... Do they talk? 1964

Phenomena of Quantum Physics: Non-Locality John Bell Colored cards: 75% Photons: ~85% ! Spontaneous correlations = ''Non-locality''... Is it useful? 1964

Quantum Cryptography from Bell's Theorem Adrian Kent Lucien Hardy Jonathan Barrett 2005 Artur Ekert 1991 Maximal Bell Violation State close to singlet (pure) Outcomes random (secret) Quantum Theory non-signaling

Can outputs be biased? PR Non-Locality plus Non-Signaling Imply Secrecy

PR Non-Locality plus Non-Signaling Imply Secrecy

PR Non-Locality plus Non-Signaling Imply Secrecy

PR Non-Locality plus Non-Signaling Imply Secrecy

Andreas Winter Lluis Masanes e.g., by space-like separation of measurement events Albert Einstein non-signaling AliceBob Efficient Causal-KD

space-like separation Andreas Winter Lluis Masanes non-signaling AliceBob Efficient Causal-KD

Stefan Wolf Renato Renner Esther Hänggi 2010 No function is good.... Amplification of NL'ty impossible Stefan Wolf Dejan Dukaric 2008 AliceBob space-like separation Efficient Causal-KD

... AliceBob space-like separation Eve ? ✔ ✔ Stefan Wolf Renato Renner Esther Hänggi 2010 Efficient Causal-KD

... efficient noise-tolerant device-independent independent of quantum physics depends only on the non-signaling AliceBob space-like separation Eve ? postulate of relativity theory ✔ ✔ recent result: two-way non-signaling condition necessary

PR Quantum boundQuantum bound Classical bound Non-signaling bound Isotropic systems Boris Cirel'son 1980 Boris Cirel'son Non-Locality: Nature Violates Bell Inequalities

PR Quantum boundQuantum bound Classical bound Non-signaling bound Isotropic systems Non-Locality: Nature Violates Bell Inequalities and Randomness Communication Complexity Collapse of Violation of Information Causality Perfect Secrecy

PR Quantum boundQuantum bound Classical bound Non-signaling bound Isotropic systems Can the Correlations Be Distilled? Paul Skrzypczyk Nicolas Brunner 2009 Dejan Dukaric 2008 Jibran Rashid

PR Quantum boundQuantum bound Classical bound Non-signaling bound Isotropic systems Can the Correlations Be Distilled? Omar Fawzi 2014 Benno Salwey

Ernst Specker 1961 Is it possible to embed the description of any physical system into classical logic? Logic and Physics

QBit Channel ? Classical Simulation of Quantum Resources: Quantum Channel

Classical Channel Classical Simulation of Quantum Resources: Quantum Channel 2 Bits Cerf Gisin Massar Toner Bacon

Classical Channel Classical Simulation of Quantum Resources: Quantum Channel, Asymptotic at most 1.28 Bits Alberto Montina

Classical Simulation of Quantum Resources: Quantum Channel, Asymptotic Kochen/ Specker model

Classical Simulation of Quantum Resources: Quantum Channel, Asymptotic Reverse Shannon Theorem: comm. rate Kochen/ Specker model

OTOT Classical Simulation of Quantum Resources: Quantum Channel Communication Value of OT = 1.28 Bits? Gisin Popescu Scarani Wolf Wullschleger 2006

Classical Channel Classical Simulation of Quantum Resources: General Asymptotic Analysis Reverse Shannon: Alberto Montina

Classical Simulation of Quantum Resources: Entanglement

Classical Simulation of Quantum Resources: Entanglement Classical Channel

Classical Simulation of Quantum Resources: Entanglement Toner Bacon 2003 Classical Channel 1 Bit

Classical Simulation of Quantum Resources: Entanglement, Asymptotic Toner Bacon 2003 Classical Channel 0.85 Bits

Classical Simulation of Quantum Resources: Entanglement, Asymptotic, Using the Kochen/Specker Model Classical Channel 0.28 Bits Alberto Montina

Classical Simulation of Quantum Resources: Non-Maximal-Entanglement Simulation Asymptotic Communication Grows with Entanglement?

Classical Simulation of Quantum Resources: Non-Maximal-Entanglement Simulation Asymptotic Communication Grows with Entanglement? Probably not

AB superluminal hidden influences David Bohm, 1951 Can Communication Explain the Correlations?

AB superluminal hidden influences David Bohm, 1951 Can Communication Explain the Correlations? Please wait until after the break...

Ernst Specker 1961 Is it possible to extend the description of a quantum-mechanical system by adding additional – fictional – propositions such that in the resulting domain, classical propositional logic governs? Logic and Physics

Ernst Specker 1961 An elementary-geometric argument shows that in general, no consistent prophecies are possible concerning the behavior of a quantum-mechanical system. Logic and Physics

Ernst Specker 1967 Simon Kochen 1961 Logic and Physics

Ernst Specker 1967 Simon Kochen M. C. Escher 1961 Logic and Physics

Ernst Specker 1967 Simon Kochen 1961 Logic and Physics

Ernst Specker 1967 Simon Kochen 1961 Logic and Physics

Ernst Specker 1967 Simon Kochen 1961 Logic and Physics

Non-Contextuality: The color of a vector is independent of the completion to a basis 1967 Simon Kochen 1961 Ernst Specker Logic and Physics

Kochen/Specker Theorem: No green-red coloring exists such that every orthonormal basis contains exactly one green vector Simon Kochen 1961 Ernst Specker Logic and Physics

Winning Condition: The output vectors are not orthogonal A Classical Winning Strategy: A Quantum Winning Strategy: Logic and Physics Renato Renner Stefan Wolf 2012

Ernst Specker 1961 In some sense, our statements deal with the scholastic speculations about the infuturabili, i.e., the question whether divine omniscience also covers what would have happened if something had happened that did not. Logic and Physics

Ernst Specker 1961 In some sense, our statements deal with the scholastic speculations about the infuturabili, i.e., the question whether divine omniscience also covers what would have happened if something had happened that did not. Logic and Physics Necessary?

Ernst Specker 1961 In some sense, our statements deal with the scholastic speculations about the infuturabili, i.e., the question whether divine omniscience also covers what would have happened if something had happened that did not. Logic and Physics Please wait until after the break... Necessary?

The Role of Randomness

What is Randomness?

The Role of Randomness What is Randomness? Please wait until after the break...

or ? ! If the measurer's choice is spontaneous then the observed color must be, too! The Role of Randomness

Randomness Determinism OR AND + no cause no choice no reality no colors Max Born, 1926 John Smolin, 2000 Hugh Everett III, 1956 David Bohm, 1951 The Role of Randomness