1. Lev Vaidman 23 August 2004, Cambridge Zion Mitrani Amir Kalev
QUBIT VERSUS BIT
Lev Vaidman
Zion Mitrani
Amir Kalev
Phys. Rev. Lett. 92, (2004),
quant-ph/
23 August 2004, Cambridge

2. BIT
QUBIT
q, f

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

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

5. Teleportation
UNKNOWN QUBIT
2 BITS

6. Teleportation
UNKNOWN QUBIT
2 BITS 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. ? or 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. ? or 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. ? or 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, (2003)

12. Measurement of the integral of a classical fieldB A

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

14. . . . . . .
… 1 0 1

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

16. What can we do with bits passing one at a time?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
The number of qubits for finding is
Quantum method yields precise result for integer I if

19. Measurement of the integral of a classical field

20. Measurement of the integral of a classical fieldB A
N qubits

21. Measurement of the integral of a classical fieldB A
N entangled qubits
Peres and Scudo
PRL (2001)

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

23. Classical uncertainty
Quantum uncertainty
Classical uncertainty

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

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

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

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

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

32. The probability of the error

33. N qubits Single particle

34. N qubits Single particle
Binary representation of k

35. N qubits Single particle
Binary representation of k
Interaction

36. N qubits Single particle
states

37. Measurement of the integral of a classical field with N bits running together
Quantum methods

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

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

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

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