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1 εναγκαλισμός-κβαντική τηλεμεταφορά εναγκαλισμός-κβαντική τηλεμεταφορά τι είναι ο εναγκαλισμός; πως γίνεται η κβαντική τηλεμεταφορά; ‘ quantum mechanics.

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Παρουσίαση με θέμα: "1 εναγκαλισμός-κβαντική τηλεμεταφορά εναγκαλισμός-κβαντική τηλεμεταφορά τι είναι ο εναγκαλισμός; πως γίνεται η κβαντική τηλεμεταφορά; ‘ quantum mechanics."— Μεταγράφημα παρουσίασης:

1 1 εναγκαλισμός-κβαντική τηλεμεταφορά εναγκαλισμός-κβαντική τηλεμεταφορά τι είναι ο εναγκαλισμός; πως γίνεται η κβαντική τηλεμεταφορά; ‘ quantum mechanics is weird” N. Bohr στα Αγγλικά: entanglement!

2 2 εναγκαλισμός

3 Οι Einstein Podolsky Rozen (EPR) το 1935 εξέτασαν αν η Κβαντική είναι ατελής η κβαντική εκτός από μη αιτιοκρατική είναι και μη τοπική! 1964: ο Bell εξέτασε αν η Κβαντική είναι τελείως λανθασμένη (ανισότητες Bell) 1980: ο A. Aspect έλεγξε πειραματικά την παραβίαση των ανισοτήτων Bell κι απέδειξε την ορθότητα της Κβαντικής! λίγη ιστορία…

4 e.g if the measurement of 1 st spin gives with probability then the second spin with certainty is also example a not entangled state: with probability then the second qubit is indetermined, it can be either or, e.g if the measurement of 1 st spin gives entangled state:

5 5συνταύτιση max entanglement entangled spins are non-separable entanglement is base-independent 1 ebit

6 6 πως παράγουμε εναγκαλισμό? plenty for photons (through a non-linear crystal) entangled polarizations light beam through a beam splitter two atoms pass through a cavity entanglement in the solid state?

7 7 κβαντική τηλεμεταφορά

8 8 κβαντικές καταστάσεις τηλεμεταφέρονται από A στο B B Ύλη και ενέργεια δεν τηλεμεταφέρονται χρειάζονται δύο βοηθητικά εναγκαλισμένα φωτόνια A A1 A2 B1 (polarization 3π/4) B2 (polarization π/4) uv photon with polarization π/4 55 m 2 Km Για να γίνει:

9 9 πώς γίνεται? A θέλει να στείλει στο B ένα qubit A B A & B δέχονται από ένα (βοηθητικό) qubit ο καθένας από μια δύο qubit entangled κατάσταση EPR e.g. A the 1 st and B the 2nd qubit δύο έχει δύο qubits ένα έχει ένα qubit

10 10   the two qubits of Alice are made to interact via a “ Bell measurement” (performed on the whole, not on each of the two qubits)   the output is random, 4 possible results: 0,π/2, π, 3π/2   we ask their relation: 00 or 01 or 10 or 11? τα μαγικά της κβαντικής! A must tell B (over the phone) which 1 out of 4 states she found (must send 2 classical bits to complete teleportation)

11 11 the EPR is a maximally entangled state so in total Alice’s Bell measurement is done in the basis “ quantum mechanics is not just words, you can only learn it by doing the maths!” instead of the usual two-qubit basis

12 12 check it! B’s qubit (third) can be written as

13 13 goes from A to B goes from A to B B has the third qubit in the right parenthesis and if A makes a Bell measurement (1 out of 4) she can tell B over the phone which state ( 1 out of 4) was obtained. Then B recovers the transferred qubit from his collapsed state (by an appropriate inverse transformation)! one of these original is destroyed during Bell measurement

14 14 τηλεμεταφέρονται καταστάσεις: φωτονίου? ατόμου? μορίου? ιού? μεγάλου αντικειμένου? πιθανό μια μέρα ??ίσως?? sci-fi! ίσως σύντομα! έγινε!

15 ένα qubit τηλεμεταφέρεται από την Αλίκη στο Bob κβαντική τηλεμεταφορά Schrodinger 1935 “entanglement is what makes quantum theory unique” ερώτημα: μπορούν να τηλεμεταφερθούν μεγαλύτερα αντικείμενα? για να γίνει απαιτούνται δύο εναγκαλισμένα qubits & δύο κλασσικά bits συμπεράσματα συμπεράσματα ο εναγκαλισμός είναι μια μετρήσιμη φυσική ποσότητα (πολύτιμη;)

16 16 one qubit superposition one qubit superposition superposition01 qubit is the quantum superposition of 0 and 1 01 but it is both 0 and 1 at the same time (0 1it is not either 0 or 1 but it is both 0 and 1 at the same time (all values between 0 and 1)! a photon goes through both slits! measurement01 after a measurement either 0 or 1 collapse of to either or

17 17 quantum interference

18 18 one spin two spins (e spin, photon polarization, 2-level atom) is their product the most general state for two qubits? NO! (only classically) a direction in space spin-1/2 states

19 19 spin-1/2 algebra "spin z up & down” "spin x up & down” "spin y up & down” x z y eigenvalues= eigenvectors

20 20 arbitrary direction n eigenvalues = eigenvectors: (the same) x z y n

21 21 quantum entanglement

22 22 two spin-1/2’s singlet triplet entanglement of two spins! (the heart of quantum information) (ground state of molecules)

23 23 singlet vs. triplet entangled states singlet anticorrelation (opposite results in every direction!) triplet anticorrelation: (only z-direction) y-dir x-dir z-dir z-dir opposite x-dir same y-dir same correlation: ( x,y-direction) look similar (can go from one to the other by rotating one of the spins) but have different sort of entanglement

24 24 singlet state (EPR pair) take two spins and move them apart (no common preparation or exchange of signals between them) and measure them in various directions (settings). What are the results? always opposite! quantum non-locality EPR paradox (1935) or quantum non-locality? common state? “strange action at a distance” or common state?

25 25 the qubit superposition01 qubit is the quantum superposition of 0 and 1 but it is both 0 and 1 at the same timeit is not either 0 or 1 but it is both 0 and 1 at the same time (randomness)! quantum information 01 qubit carries quantum information (all intermediate values between 0 and 1)! measurement01 ( after a measurement: either 0 or 1 (certainty) collapse of to either or

26 26 beam splitter two-slit experiment 50%50% 100%0% interference no interference

27 27problems from the Pauli algebra of prove that rotation by θ around x-axis is (check for rotations by π, 2π, 4π). Solve the Schr. eqn. for const. magnetic field B along the x-axis which leads to the unitary evolution prove for the projection operators and the probabilities for time-dependent field magnetic field solve the problem directly!

28 28 quantum physics quantum physics would be deterministic (but Heisenberg’s uncertainty principle!) if one could clone an unknown quantum state would violate relativity relativity would have absolute time (but no messages travel faster than light!) the no cloning theorem is essential for quantum physics & relativity!

29 29 beam splitter two-slit experiment 50%50% 100%0%

30 30 one qubit (interference) one qubit (interference) superposition01 qubit is the quantum superposition of 0 and 1 01 but it is both 0 and 1 at the same time (0 1it is not either 0 or 1 but it is both 0 and 1 at the same time (all values between 0 and 1)! a photon goes through both slits! measurement01 after a measurement either 0 or 1 collapse of to either or QM is probabilistic!

31 31 (EPR) Einstein Podolsky Rozen (1935): is QM incomplete? No! is nonlocal! Bell (1964) asked if QM is wrong? No! Violation of Bell’s inequalities was tested experimentally by A. Aspect (1980) showing that QM is correct! more qubits (entanglement) QM is non-local!

32 32 spin-1/2 reminder!

33 33spin-1/2 Stern-Gerlach apparatus qubit: “spin up” “spin down” probability measurement

34 34 spin-1/2 algebra "spin z up & down” "spin x up & down” "spin y up & down” x z y eigenvalues= eigenvectors

35 35 arbitrary direction n eigenvalues = eigenvectors: (the same) x z y n

36 36 two spin-1/2’s singlet triplet entanglement of two spins! (the heart of quantum information) (ground state of molecules)

37 37 one spin two spins (e spin, photon polarization, 2-level atom) is their product the most general state for two qubits? NO! (only classically) a direction in space spin-1/2 states

38 38 two spin-1/2 entanglement a state of two spins 1& 2 is entangled if a state of two spins 1& 2 is entangled if by measuring one spin you can also determine the other (not sufficient!) is non-separable is entangled (if you measure 1 st you get the opposite result for 2 nd, even if you separate them very far apart) e.g.

39 39 singlet vs. triplet entangled states singlet anticorrelation (opposite results in every direction!) triplet anticorrelation: (only z-direction) y-dir x-dir z-dir z-dir opposite x-dir same y-dir same correlation: ( x,y-direction) look similar (can go from one to the other by rotating one of the spins) but have different sort of entanglement

40 40 matter & energy matter & energy cannot teleport from A to B (cannot be transferred without passing through intermediate locations) copying? no! scanning violates Heisenberg’s uncertainty (no cloning theorem) quantum states quantum states (ultimate structure) can teleport (without passing through intermediate locations) no, because:

41 41 copying? no! scanning violates Heisenberg’s uncertainty (no cloning theorem) no, because: quantum cloning is impossible quantum cloning is impossible

42 42 singlet state (EPR pair) take two spins and move them apart (no common preparation or exchange of signals between them) and measure them in various directions (settings). What are the results? always opposite! quantum non-locality EPR paradox (1935) or quantum non-locality? common state? “strange action at a distance” or common state?


Κατέβασμα ppt "1 εναγκαλισμός-κβαντική τηλεμεταφορά εναγκαλισμός-κβαντική τηλεμεταφορά τι είναι ο εναγκαλισμός; πως γίνεται η κβαντική τηλεμεταφορά; ‘ quantum mechanics."

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