Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations In the process theory of relations : • system-types are sets A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 11 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations In the process theory of relations : • system-types are sets • processes are relations { x , y , z } a �→ x = a �→ y R b �→ z { a , b , c } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 11 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations In the process theory of relations : • system-types are sets • processes are relations { x , y , z } a �→ x = a �→ y R b �→ z { a , b , c } • ...which we can think of as non-deterministic computations: { x , y , z } a �→ { x , y } = b �→ z R c �→ ∅ { a , b , c } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 11 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations Relations compose in sequentially just like you learned in school: R S S ◦ R b 1 a 1 c 1 a 1 c 1 b 2 a 2 c 2 a 2 c 2 � b 3 a 3 c 3 a 3 c 3 b 4 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 12 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations ...and they compose in parallel via the cartesian product. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 13 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations ...and they compose in parallel via the cartesian product. • that is, systems compose like this: A B A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 13 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations ...and they compose in parallel via the cartesian product. • that is, systems compose like this: := { ( a , b ) | a ∈ A , b ∈ B } A B A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 13 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example: relations ...and they compose in parallel via the cartesian product. • that is, systems compose like this: := { ( a , b ) | a ∈ A , b ∈ B } A B • so relations compose like this: :: ( a , b ) �→ ( c , d ) ⇐ ⇒ :: a �→ c and :: b �→ d R S R S A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 13 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} • ...because: = { ( a , • ) | a ∈ A } ∼ = A = A A A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} • ...because: = { ( a , • ) | a ∈ A } ∼ = A = A A • processes from ‘no wire’ represent (non-deterministic) states A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} • ...because: = { ( a , • ) | a ∈ A } ∼ = A = A A • processes from ‘no wire’ represent (non-deterministic) states, e.g. for a bit: � = • �→ 0 0 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} • ...because: = { ( a , • ) | a ∈ A } ∼ = A = A A • processes from ‘no wire’ represent (non-deterministic) states, e.g. for a bit: � � = • �→ 0 = • �→ 1 0 1 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ‘no wire’ is a one-element set: := {•} • ...because: = { ( a , • ) | a ∈ A } ∼ = A = A A • processes from ‘no wire’ represent (non-deterministic) states, e.g. for a bit: � � � = • �→ 0 = • �→ 1 = • �→ { 0 , 1 } ∗ 0 1 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 14 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ...whereas processes to ‘no wire’ are called effects. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 15 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ...whereas processes to ‘no wire’ are called effects.These test for the given state(s): � 0 = 0 �→ • A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 15 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ...whereas processes to ‘no wire’ are called effects.These test for the given state(s): � � 0 1 = 0 �→ • = 1 �→ • A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 15 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ...whereas processes to ‘no wire’ are called effects.These test for the given state(s): � � � 0 1 ∗ = 0 �→ • = 1 �→ • = { 0 , 1 } �→ • • when state meets effect, there are two possibilities: T T � = • �→ • = ∅ S S A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 15 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Some processes in relations • ...whereas processes to ‘no wire’ are called effects.These test for the given state(s): � � � 0 1 ∗ = 0 �→ • = 1 �→ • = { 0 , 1 } �→ • • when state meets effect, there are two possibilities: T T � = • �→ • = ∅ S S These stand for true and false . A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 15 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation States on two systems • States on two systems are more interesting A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 16 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation States on two systems • States on two systems are more interesting, e.g.: � := ∗ �→ { (0 , 0) , (1 , 1) } ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 16 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation States on two systems • States on two systems are more interesting, e.g.: � := ∗ �→ { (0 , 0) , (1 , 1) } ψ Interpretation: “I don’t know what bit I have, but I know its the same as yours” A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 16 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation States on two systems • States on two systems are more interesting, e.g.: � := ∗ �→ { (0 , 0) , (1 , 1) } ψ Interpretation: “I don’t know what bit I have, but I know its the same as yours” • States of the two systems no longer have their own, separate identities A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 16 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation States on two systems • States on two systems are more interesting, e.g.: � := ∗ �→ { (0 , 0) , (1 , 1) } ψ Interpretation: “I don’t know what bit I have, but I know its the same as yours” • States of the two systems no longer have their own, separate identities • Hence we get... A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 16 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Outline Process theories Non-separability One-time pad Quantum teleportation A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 17 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Separable states • A state ψ on two systems is separable if there exist ψ 1 , ψ 2 such that: = ψ 1 ψ 2 ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 18 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Separable states • A state ψ on two systems is separable if there exist ψ 1 , ψ 2 such that: = ψ 1 ψ 2 ψ • Intuitively: the properties of the system on the left are independent from those on the right A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 18 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Separable states • A state ψ on two systems is separable if there exist ψ 1 , ψ 2 such that: = ψ 1 ψ 2 ψ • Intuitively: the properties of the system on the left are independent from those on the right • In the deterministic-land, all states to separate... A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 18 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability • ...which is why non-separable states are way more interesting! A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 19 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability • ...which is why non-separable states are way more interesting! • But, how do we know we’ve found one? A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 19 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability • ...which is why non-separable states are way more interesting! • But, how do we know we’ve found one? • i.e. that there do not exist states ψ 1 , ψ 2 such that: = ψ 1 ψ 2 ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 19 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability • ...which is why non-separable states are way more interesting! • But, how do we know we’ve found one? • i.e. that there do not exist states ψ 1 , ψ 2 such that: = ψ 1 ψ 2 ψ • Problem: Showing that something doesn’t exist is hard. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 19 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability Solution: Replace a negative property with a postive one: A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 20 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Characterising non-separability Solution: Replace a negative property with a postive one: Definition A state ψ is called cup-state if there exists an effect φ , called a cap-effect , such that: φ φ = = ψ ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 20 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Cup-states • By introducing some clever notation: φ := := ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 21 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Cup-states • By introducing some clever notation: φ := := ψ • Then these equations: φ φ = = ψ ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 21 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Cup-states • By introducing some clever notation: φ := := ψ • Then these equations: φ φ = = ψ ψ • ...look like this: = = A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 21 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Yank the wire! = = A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 22 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Yank the wire! = = A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 22 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example • In relations , there is an obvious choice of cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 23 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example • In relations , there is an obvious choice of cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } • The associated cap-effect corresponds to “checking if two bits are the same”: � := { (0 , 0) , (1 , 1) } �→ ∗ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 23 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Example • In relations , there is an obvious choice of cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } • The associated cap-effect corresponds to “checking if two bits are the same”: � := { (0 , 0) , (1 , 1) } �→ ∗ • This, plus NOT... � 0 �→ 1 := NOT 1 �→ 0 ...gives us enough to start building interesting stuff. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 23 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Outline Process theories Non-separability One-time pad Quantum teleportation A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 24 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside • Aleks wants to send a bit to Bob, but is paranoid (as usual) A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside • Aleks wants to send a bit to Bob, but is paranoid (as usual) • He opens his envelope, and tells Bob if the bit inside is the same as the one he wants to send A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside • Aleks wants to send a bit to Bob, but is paranoid (as usual) • He opens his envelope, and tells Bob if the bit inside is the same as the one he wants to send • Bob opens his envelope, and: A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside • Aleks wants to send a bit to Bob, but is paranoid (as usual) • He opens his envelope, and tells Bob if the bit inside is the same as the one he wants to send • Bob opens his envelope, and: • if the bits matched before, Bob now has Aleks’ bit, A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation An incredibly sophisticated security protocol • Suppose Aleks and Bob each have an envelope with the same (random) bit sealed inside • Aleks wants to send a bit to Bob, but is paranoid (as usual) • He opens his envelope, and tells Bob if the bit inside is the same as the one he wants to send • Bob opens his envelope, and: • if the bits matched before, Bob now has Aleks’ bit, • otherwise he flips the bit. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 25 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad with relations • we can represent the envelopes with the shared random bit as a cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 26 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad with relations • we can represent the envelopes with the shared random bit as a cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } • then checking whether two bits are the same is a ‘ measurement ’ that Aleks can perform on his systems A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 26 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad with relations • we can represent the envelopes with the shared random bit as a cup-state: � := ∗ �→ { (0 , 0) , (1 , 1) } • then checking whether two bits are the same is a ‘ measurement ’ that Aleks can perform on his systems • There are two possible outcomes: := “the same” , := “NOT the same” NOT A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 26 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad with relations • ...which we can write as: := & := U i U 0 U 1 NOT i ∈{ 0 , 1 } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 27 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad with relations • ...which we can write as: := & := U i U 0 U 1 NOT i ∈{ 0 , 1 } • Then, the U i satisfy: U i = U i A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 27 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad diagram So, the OTP protocol looks like this: U i U i b A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 28 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation One-time pad diagram So, the OTP protocol looks like this: Aleks Bob U i Bob’s fix Aleks’ “measurement” envelope 1 U i envelope 2 Aleks’ bit ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 28 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob U i U i b A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 29 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob U i U i b A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 29 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob U i U i b A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 29 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob b A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 29 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Outline Process theories Non-separability One-time pad Quantum teleportation A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 30 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • We go from classical to quantum by changing the process theory: relations ⇒ quantum maps A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 31 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • We go from classical to quantum by changing the process theory: relations ⇒ quantum maps • The quantum analogue to a bit is a qubit, which represents the state of the simplest non-trivial quantum system A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 31 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • We go from classical to quantum by changing the process theory: relations ⇒ quantum maps • The quantum analogue to a bit is a qubit, which represents the state of the simplest non-trivial quantum system • Example: polarization of a photon A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 31 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • The state space of a bit consists of two points: 0 and 1 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 32 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • The state space of a bit consists of two points: 0 and 1 • ...whereas qubits, it forms a sphere: 0 θ ψ α 1 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 32 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum bits • The state space of a bit consists of two points: 0 and 1 • ...whereas qubits, it forms a sphere: 0 θ ψ α 1 • “Plain old” bits live at the North Pole and the South Pole. A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 32 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum entanglement • In quantum-land, we can realise a ‘cup’ using quantum entanglement ⇐ = “Bell state” A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 33 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum entanglement • In quantum-land, we can realise a ‘cup’ using quantum entanglement ⇐ = “Bell state” • Even though this thing is (slightly) more complicated to describe, it acts just like before A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 33 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum measurement • We also have a quantum analogue for Aleks’ measurement: ⇐ = “Bell measurement” U i i ∈{ 0 , 1 , 2 , 3 } A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 34 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation Quantum measurement • We also have a quantum analogue for Aleks’ measurement: ⇐ = “Bell measurement” U i i ∈{ 0 , 1 , 2 , 3 } where there are now three different ways to “NOT”: := := U 0 U 1 := := U 2 U 3 A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 34 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation OTP ⇒ quantum teleportation Aleks Bob Bob’s fix U i Aleks’ “measurement” envelope 1 U i envelope 2 Aleks’ bit ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 35 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation OTP ⇒ quantum teleportation Aleks Bob U i Bob’s fix Bell measurement U i quantum state ψ Bell state A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 35 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob U i U i ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 36 / 38
Process theories Non-separability Radboud University Nijmegen One-time pad Quantum teleportation ...and it works Aleks Bob U i U i ψ A. Kissinger 23rd November 2016 Quantum teleportation, diagrams, and the one-time pad 36 / 38
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