Bevezetés a kvantum-informatikába és kommunikációba 2014/2015 tavasz. Mérés, NCT, kvantumállapot március 12.

Transcription

1 Bevezetés a kvantum-informatikába és kommunikációba 2014/2015 tavasz Mérés, NCT, kvantumállapot március 12.

2 Tegnap még összefonódtam, mára megmértek

3 Slides for Quantum Computing and Communications An Engineering Approach Sándor Imre Ferenc Balázs

4 3 rd Postulate using ket notations Measurement statistic Post measurement state Completeness relation

5 Measurement operators and the 3 rd Postulate in case of projective measurements 3 rd Postulate with projectors

6 POVM and the 3 rd Postulate Measurement statistic Post measurement state Unknown and/or indifferent! Completeness relation

7 POVM construction example Our two non-orthogonal states are: Based on the indirect construction approach we try to ensure that To achieve this we need

8 POVM construction example To fulfil the completeness relation

9 Completeness relation OK since

10 D 2 must be positive semi-definite is very promising, but unfortunately wrong!

11 How to apply POVM operators - 0 and 1 has the same importance It requires

12 How to apply POVM operators - minimising uncertainty Goal: to minimise Assuming

13 How to apply POVM operators - minimising uncertainty Copyright 2005 John Wiley & Sons Ltd.

14 How to apply POVM operators - false alarm vs. not happen alarm It is assumed that detecting 1 correctly is much more important Copyright 2005 John Wiley & Sons Ltd.

15 Generalisation of POVM

16 Relations among the measurement types Projective measurement can be regarded as a special POVM. Clearly speaking POVM is a generalised measurement without the interest of post-measurement state + construction rules. Neumark s extension: any generalised measurement can be implemented by means of a projective measurement + auxiliary qbits + unitary transform.

17 Relations among the measurement types Copyright 2005 John Wiley & Sons Ltd.

18 No Cloning (Copy) Theorem "Knowledge is what we get when an observer, preferably a scientifically trained observer, provides us with a copy of reality that we can all recognize. " Christopher Lasch

19 Existence of universal quantum copy machine 1 Copyright 2005 John Wiley & Sons Ltd. Upper wire: quantum state to be cloned. Middle wire: auxiliary qubits. Lower wire: environment. We are interested whether such an U exists at all? If the answer is YES then we are going to search for Q.

20 Existence of universal quantum copy machine 2 Making a copy means: U must be unitary i.e. it preserves the inner product. For input For output The two inner products are the same if

21 No cloning theorem No quantum gate exists which is able to copy quantum states from an unknown and arbitrary set of states! But Orthogonal (e.g. classical states, or Bell pairs) can be copied in compliance with our everyday computer practice. Arbitrary but known states can also be copied (see the forthcoming slides).

22 How to Prepare an Arbirary Superposition "By failing to prepare, you are preparing to fail." Benjamin Franklin "I m just preparing my impromptu remarks. Winston Churchill

23 Abstract quantum circuit of the generalised interferometer 1 Copyright 2005 John Wiley & Sons Ltd.

24 Abstract quantum circuit of the generalised interferometer 2 Copyright 2005 John Wiley & Sons Ltd.

25 Abstract quantum circuit of the generalised interferometer 3 Copyright 2005 John Wiley & Sons Ltd.

26 Abstract quantum circuit of the generalised interferometer 4 Copyright 2005 John Wiley & Sons Ltd.

27 Abstract quantum circuit of the generalised interferometer 4 Copyright 2005 John Wiley & Sons Ltd. We managed to produce an almost arbitrary state, the only restriction is related to the global phase. The global phase, however, does not influence measurement statistic.

28 Dr. Bacsárdi László, BME

29 Kvantum-áramkör Dr. Bacsárdi László, BME

30 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

31 Dr. Bacsárdi László, BME Teleportálás

32 Dr. Bacsárdi László, BME Teleportálás

33 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

34 Alkalmazzuk L. Bacsardi, D. Banyai, S. Imre, Analyzing Communication in Quantum Based Mobile Ad Hoc Networks, AQIS'13 - Asian Quantum Information Science Conference. Chennai, India, pp L. Bacsardi, Quantum Based Solutions for Efficient Communication Networks, IEEE 17th International Conference on Intelligent Engineering Systems, Monte de la Cruz, Costa Rica, IEEE, pp Dr. Bacsárdi László, BME

35 Slides for Quantum Computing and Communications An Engineering Approach Chapter 4 Sándor Imre Ferenc Balázs

36 Motto "The fastest algorithm can frequently be replaced by one that is almost as fast and much easier to understand. Neil D. Jones

37 Superdense Coding

38 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.

39 Copyright 2005 John Wiley & Sons Ltd. The architecture