2. kiszh időpont változás

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2 2. kiszh időpont változás április 20. HELYETT április 13-án lesz!

3 kiszh feladatok megoldása

4 Időnként érdemes körülnézni

5 A kvantummechanika Posztulátumai, avagy, ahogy az apró dolgok működnek 1. Posztulátum: kvantum bit Hilbert-tér 2. Posztulátum: logikai kapuk Unitér transzformáció Elemi kvantum logikai kapuk 3. Posztulátum: Q/C átalakítás Mérési statisztika Mérés utáni állapot 4. Posztulátum: regiszterek Tenzor szorzás

6 Újdonságok Egy izgalmas következmény: Összefonódás Egy elgondolkodtató következmény: No cloning tétel Mérnöki megközelítés: Projektív és POVM mérés-konstrukció Mindez színesben: Kitekintés

7 Superdense Coding

8 Szupersűrűségű tömörítés 1992: elmélet 1996: sikeres kísérlet Bennett, C. H. & Wiesner, S. J. Communication via one- and two-particle operators on Einstein Podolsky Rosen states. Phys. Rev. Lett. 69, (1992). Mattle, K. et al. Dense coding in experimental quantum communication. Phys. Rev. Lett. 76, (1996). Dr. Bacsárdi László, BME

9 The goal From classical information theory point of view the information transmission rate is limited. Alice and Bob would like to increase the rate of information transfer by means of quantum communications exploiting such special properties as antanglement.

10 Copyright 2005 John Wiley & Sons Ltd. The architecture

11 Protocol steps 1 First the share a entangled pair. Next Alice applies the following a special coding scheme on her half pair and sends the her coded qubit to Bob.

12 Protocol steps 2 Bob being an expert of quantum computing realises that the modified pairs represent the four different Bell pairs therefore they for an othonormal set of quantum states. The can be unambiguously distinguished by means of a projective measurement. However there is another way to solve the detection problem if we exploit the unitary nature of quantum transformations i.e. we are able to compute the inverse transformation.

13 Protocol steps 3 We know that Bell states can be produced by means of the following circuit Copyright 2005 John Wiley & Sons Ltd.

14 Protocol steps 3 Since both and gates are Hermitian operators Bob has to implement these gates in the reverse order to build the decoder.

15 Quantum teleportation

16 Dr. Bacsárdi László, BME Teleportálás

17 1993: elmélet Teleportálás 1998: sikeres kísérlet 2004: 600 méter 2012: 97 km (Kína) 2012: 143 km (Kanári-szigetek) C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, Teleporting an Unknown Quantum State via Dual Classical and Einstein- Podolsky-Rosen Channels, Phys. Rev. Lett. 70, (1993) Juan Yin et. al, Quantum teleportation and entanglement distribution over 100-kilometre free-space channels, Nature (2012) Ma, X. S.; Herbst, T.; Scheidl, T.; Wang, D.; Kropatschek, S.; Naylor, W.; Wittmann, B.; Mech, A. et al. (2012). "Quantum teleportation over 143 kilometres using active feed-forward". Nature 489 (7415): C. Nölleke, A. Neuzner, A. Reiserer, C. Hahn, G. Rempe, S. Ritter}, Efficient Teleportation Between Remote Single-Atom Quantum Memories, Phys. Rev. Lett. 110, (2013) Dr. Bacsárdi László, BME

18 Definitions There is an often repeated scene in most popular science fiction novels and movies. The space traveller enters into a cabin on the board of a space ship than he/she suddenly disappears accompanied with colorful lighting effects. A few moments later our astronaut appears in another cabin located on a planet hundreds of light-years away from the starting point. Let us analyze this futuristic scene scientifically.

19 Alternative 1 On one hand we can break the traveller into smaller parts say to elementary particles such as electrons, protons, etc. in the departure cabin. As we have learned earlier these particles obey quantum mechanics and thus each of them can be represented as a one-qbit superposition. Therefore we need a quantum communication channel between the two locations to transfer the components of our daring astronaut. Finally he/she has to be rebuilt in the arrival cabin from the original particles. This approach requires an error-free channel (more precisely error-free communication protocol) unless we would like to meet with a monster.

20 Alternative 2 On the other hand we are able to replace quantum communications with classical one and utilize our related broad knowledge. To follow this way we have to ensure and encode the state of each particle and only this classical information will be delivered between the two cabins. In the destination cabin a stockpile of particles are required from which the traveller can be rebuilt in compliance with the transferred assembly manual. Unfortunately this idea also suffers some drawbacks. The most challenging one is how the states of the particles can be measured? Theoretically we need infinite number of measurements to estimate the corresponding probability amplitudes with arbitrary small inaccuracy. Finally we can conclude that neither method seems to be mature enough for practical implementation, if only...

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22 Teleportation C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels Phys. Rev. Lett. 70, (1993)

23 Steps of teleportation - initialisation Copyright 2005 John Wiley & Sons Ltd.

24 Steps of teleportation - entanglement Copyright 2005 John Wiley & Sons Ltd.

25 Steps of teleportation - entanglement Copyright 2005 John Wiley & Sons Ltd.

26 Steps of teleportation - measurement Copyright 2005 John Wiley & Sons Ltd.

27 Steps of teleportation - how to reassembly?

28 Remarks

29 Rejtvény teleportálós másoló