A central problem in cryptography: the key distribution problem.

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1 Scientific American 314, (2016) A central problem in cryptography: the key distribution problem. Mathematics solution: public key cryptography. Public-key cryptography relies on the computational difficulty of certain hard mathematical problems (for example factoring) Security problems with public key cryptography: (1) The is no proof that there is no easy solution to factoring: somebody can come up with new much quicker algorithm! (2) Quantum computer, if build, can break public key encryption fast quantum algorithm is already knows (Shor s algorithm) 1

2 Another solution to the key distribution problem: Quantum key distribution Use quantum communication channel: physical system capable delivering quantum systems more or less intact from one place to another. What is this quantum system? Photons! Why is this secure: Quantum mechanics: quantum bits cannot be copied or monitored. Any attempt to do so will result in altering it that can not be corrected. How to use photons as qubits? Use polarization of photons to encode 0 and 1. Electromagnetic waves A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector E (red) oscillating in the vertical direction. The magnetic field B (or H) is always at right angles to it (blue), and both are perpendicular to the direction of propagation (z)

3 Quantum key distribution 3

4 Scientific American 314, (2016) Scientific American 314, (2016) 4

5 Quantum key distribution Scientific American 314, (2016) Scientific American 292, 78 (2005) 5

6 Scientific American 292, 78 (2005) Entanglement-based Quantum Key Distribution set-up connecting the two Canary Islands La Palma and Tenerife. The optical link is 144 km long. OGS, optical ground station; GPS, Global Positioning System; PBS, polarizing beamsplitter; BS, beamsplitter; HWP, half-wave plate. Ursin, R. et al. Nature Phys. 3, (2007). 6

7 Problems with quantum key distribution Qubits can not be copied we can not amplify the signal or retransmit information as in the classical case. If you can not copy teleport! 7

8 Quantum teleportation What is it? Technique for moving quantum states around, even in an absence of quantum communication channel. The problem: Alice must deliver qubit to Bob She does not know the state of the qubit She can use only classical channels 8

9 9

10 Quantum repeater is essentially a small quantum computer! Quantum internet? Quantum repeater is essentially a small quantum computer So need to be able to implement small-scale quantum computing for quantum communications too!

11 What do we need to build a quantum computer? The DiVincenzo criteria Qubits which retain their properties. Scalable array of qubits. Initialization: ability to prepare one certain state repeatedly on demand. Need continuous supply of 0. Universal set of quantum gates. A system in which qubits can be made to evolve as desired. Long relevant decoherence times. Ability to efficiently read out the result. Interconvert stationary and flying qubits Transmit flying qubits between distant locations What do we need to build a quantum computer? Need to precisely control quantum systems 11

12 Quantum Computer (Innsbruck) P 1/2 D 5/2 quantum bit S 1/2 Courtesy of the R. Blatt s Innsbruck group Qubits with trapped ions Encoding of quantum information requires long-lived atomic states: optical transitions Ca +, Sr +, Ba +, Ra +, Yb +, Hg + etc. microwave transitions 9 Be +, 25 Mg +, 43 Ca +, 87 Sr +, 137 Ba +, 111 Cd +, 171 Yb + P 1/2 D 5/2 P 3/2 S 1/2 qubit S 1/2 qubit 12

13 String of Ca + ions in linear Paul trap Row of qubits in a linear Paul trap forms a quantum register ω z ω x, y MHz MHz 50 µm 13

14 Linear crystal of 20 confined atomic 171 Yb+ ions laser cooled to be nearly at rest C. Monroe, and J. Kim Science 2013;339:

15 Quantum Control: measuring and manipulation of individual quantum systems 2012 Nobel prize David Wineland Picture of a string of ions Ca + 3d 5/2 Serge Haroche nobel.org Making quantum superposition of two ions Scaling up: Concept of a quantum CCD trap Image credit: National Institute of Standards and Technology C. Monroe, and J. Kim Science 2013;339:

16 Scaling up: Modular distributed quantum computer Several elementary logic units (ELU)s are connected through a photonic network by using an optical crossconnect switch, inline fiber beamsplitters, and a photon-counting imager. C. Monroe, and J. Kim Science 2013;339:

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