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QUBIT VERSUS BIT

QUBIT VERSUS BIT. Lev Vaidman. Zion Mitrani Amir Kalev. Phys. Rev. Lett. 92 , 217902 (2004),. quant-ph/0406024. 23 August 2004, Cambridge. BIT. QUBIT. q, f. BIT. QUBIT. q, f. TO WRITE q, f. TO WRITE 0, 1. TO READ 0, 1. TO READ 0, 1. NO!. N. N. N. N. N. N/2.

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QUBIT VERSUS BIT

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  1. QUBITVERSUSBIT Lev Vaidman Zion Mitrani Amir Kalev Phys. Rev. Lett.92, 217902 (2004), quant-ph/0406024 23 August 2004, Cambridge

  2. BIT QUBIT q, f

  3. BIT QUBIT q, f TO WRITE q, f TO WRITE 0, 1 TO READ 0, 1 TO READ 0, 1 NO!

  4. N N N N N N/2 DENSE CODING N/2 N N KNOWN QUBITS

  5. Teleportation 2 BITS UNKNOWN QUBIT

  6. Teleportation 2 BITS UNKNOWN QUBIT 2

  7. We cannot store and retrieve more than one bit in a qubit HOLEVO What can we do with a qubit that we cannot do with a bit?

  8. We cannot store and retrieve more than one bit in a qubit HOLEVO What can we do with a qubit that we cannot do with a bit? Tasks with 2 possible outcomes We know ? or

  9. We cannot store and retrieve more than one bit in a qubit HOLEVO What can we do with a qubit that we cannot do with a bit? Tasks with 2 possible outcomes We know ? or

  10. We cannot store and retrieve more than one bit in a qubit HOLEVO What can we do with a qubit that we cannot do with a bit? Tasks with 2 possible outcomes We know ? or

  11. Measurement of the parity of the integral of a classical field Galvao and Hardy,Phys. Rev. Lett. 90, 087902 (2003)

  12. Measurement of the integral of a classical field B A

  13. Measurement of the integral of a classical field B A Binary representation of I . … 1 0 1 . . . . .

  14. . . . . . . 0 0 0 0 0 … 1 0 1

  15. What can we do with bits passing one at a time? B A

  16. What can we do with bits passing one at a time? B or A • We can “write” a real number in a bit as the probability of its flip

  17. Uncertainty in measurement with bits Optimization for The number of bits for finding is

  18. Uncertainty in measurement with bits Optimization for The number of bits for finding is is The number of qubits for finding Quantum method yields precise result for integerI if

  19. Measurement of the integral of a classical field

  20. Measurement of the integral of a classical field B A N qubits

  21. Measurement of the integral of a classical field B A N entangled qubits Peres and Scudo PRL 86 4160 (2001)

  22. But the digital method works much better! B A . . . . . .

  23. Quantum uncertainty Classical uncertainty

  24. Information about I in N qubits is in Can we use a single particle in a superposition of N different states instead? . . . . . . . . .

  25. No. Hilbert space is too small: Information about I in N qubits is in Can we use a single particle in a superposition of N different states instead? . . . . . . . . .

  26. Measurement of the integral of a classical field with a single particle in a superposition of states

  27. Measurement of the integral of a classical field with a single particle in a superposition of states

  28. Measurement of the integral of a classical field with a single particle in a superposition of states Measurement yields

  29. The probability of the error

  30. N qubits Single particle

  31. N qubits Single particle Binary representation of k

  32. N qubits Single particle Binary representation of k Interaction

  33. N qubits Single particle states

  34. Quantum methods Measurement of the integral of a classical field with N bits running together B A

  35. How to read a string of length out of strings using a single particle?

  36. How to read a string of length out of strings using a single particle? 1 0

  37. How to read a string of length out of strings using a single particle? 1 0 Bits instead We need at least

  38. What else can we do with the quantum phase?

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