QUANTUM MECHANICS AND QUANTUM INFORMATION SCIENCE

1. QUANTUM MECHANICS AND QUANTUM INFORMATION SCIENCE WHAT IS Ψ?

2. IS Ψ ONTIC OR EPISTEMIC? • WHAT IS A QUANTUM MEASUREMENT?

3. QUANTUM PARADOXES • THE DOUBLE-SLIT: WAVE-PARTICLE DUALITY (1905-1927-) • SCHRöDINGER CAT (1035) • EPR PARADOX AND QUANTUM ENTANGLEMENT (1935)

4. INTERPRETATIONS • BOHR VS VON NEUMANN/DIRAC • EVERETT (MANY WORLDS?) (1957-) • HIDDEN VARIABLES (1935-) • OTHERS (MODAL, CONSISTENT HISTORIES, ETC)

5. NO-GO THEOREMS FOR HIDDEN VARIABLES • VON NEUMANN THEOREM (1932) • BELL’S THEOREM (1964) • KOCHEN-SPECKER THEOREM (1967) CONTEXTUAL HVT ARE INCOMPATIBLE WITH QM HOWEVER, BOHM’S HIDDEN VARIABLE THEORY IS NOT RULED OUT BY THESE THEOREMS

6. BELL’S THEOREM STANDARD OR ORTHODOX QUANTUM MECHANICS IS INCOMPATIBLE WITH LOCAL REALISM (USES LOCAL HIDDEN VARIABLES)

7. EINSTEIN’S 1927 ARGUMENT USES A SINGLE PARTICLE

8. EINSTEIN’S 1927 ARGUMENT Ψ = (1/√2) [ψa + ψb] p(1a Λ 1b |ψ) = p (1a|ψ) p(1b|1a,ψ) = p(1a|ψ) p(1b|ψ) locality = ¼ THIS CONTRADICTS THE STANDARD QM PREDICTION p(1aΛ 1b |ψ) = 0

9. BIRTH OF QUANTUM INFORMATION AGE 1982 FEYNMAN SHOWED THAT A CLASSICAL TURING MACHINE WOULD EXPERIENCE EXPONENTIAL SLOW DOWN WHEN SIMULATING QUANTUM PROCESSES BUT HIS HYPOTHETICAL UNIVERSAL QUANTUM SIMULATOR WOULD NOT. 1985 DAVID DEUTSCH DEFINED A UNIVERSAL QUANTUM COMPUTER 1996 SETH LLOYD SHOWED THAT A QUANTUM COMPUTER CAN BE PROGRAMMED TO SIMULATE ANY LOCAL QUANTUM SYSTEM EFFICIENTLY.

10. BITS AND QUBITS IN QUANTUM COMPUTING THE ANALOGUE OF THE CLASSICAL UNIT OF INFORMATION, THE BIT, IS A QUBIT WHICH IS A TWO-LEVEL QUANTUM SYSTEM LIKE THE TWO STATES OF POLARIZATION OF A SINGLE PHOTON WHICH CAN BE IN A SUPERPOSITION OF STATES: |ψ> = α|0> + β|1> with | α|2 + | β |2 = 1

11. BREAKTHROUGHQUANTUM ALGORITHMS 1992 DEUTSCH-JOZSA: exponentially faster than any deterministic classical algorithm 1998 improved by CLEVE, EKERT, MACCHIAVELLO and MOSCA 1994 SHOR: integer factorization 1996 GROVER: quantum search

12. OTHER ALGORITHMS FOR QUANTUM FOURIER TRANSFORM QUANTUM GATES QUANTUM ADIABATIC QUANTUM ERROR CORRECTION

13. NO-CLONING THEOREM WOOTERS, ZUREK, DIEKS (1982) QUANTUM MECHANICS FORBIDS THE CREATION OF IDENTICAL COPIES OF AN UNKNOWN QUANTUM STATE

14. NO-DELETING THEOREM A K PATI & S L BRAUNSTEIN, NATURE 2000 GIVEN TWO COPIES OF SOME UNKNOWN AND ARBITRARY QUANTUM STATE, IT IS IMPOSSIBLE TO DELETE ONE OF THE COPIES IT IS A TIME REVERSED DUAL TO THE NO-CLONING THEOREM IN SOME INSTANCES QUANTUM STATES CAN BE ROBUST

15. QUANTUM INFORMATION PROCESSING SCIENCE • QUANTUM COMPUTING • QUANTUM COMPLEXITY THEORY • QUANTUM CRYPTOGRAPHY • QUANTUM ERROR CORRECTION • QUANTUM COMMUNICATION COMPLEXITY • QUANTUM ENTANGLEMENT • QUANTUM DENSE CODING

16. QUANTUM ENTANGLEMENT: CHIEF RESOURCE IN QI SCIENCE NON-SEPARABLE STATES COMPLETE KNOWLEDGE OF THE STATE DOES NOT IMPLY COMPLETE KNOWLEDGE OF THE PARTS STRONG MEASUREMENT RESULTS IN CONDITIONAL DISJUNCTION OF THE STATE

17. POVMs IN QI PROCESSING CONVENTIONAL PROJECTIVE MEASUREMENT IS REPLACED BY MORE GENERAL POVMs: CHOICE OF NON-ORTHOGONAL BASIS FOR MEASUREMENTS WITH THE NEW PROJECTORS STILL SUMMING TO UNITY REASON: PROJECTIVE MEASUREMENTS ON A LARGER SYSTEM, DESCRIBED BY A PROJECTION-VALUED MEASURE (PVM), WILL ACT ON A SUB-SYSTEM IN WAYS THAT CANNOT BE DESCRIBED BY A PVM ON THE SUB-SYSTEM ALONE

18. ENTANGLEMENT MEASURES BELL INEQUALITY VIOLATION IS A MEASURE OF ENTANGLEMENT BUT NOT ALL ENTANGLED STATES VIOLATE BIs. A WERNER STATE, A MIXTURE OF THE MAXIMALLY ENTANGLED STATE AND THE MAXIMALLY MIXED STATE, CAN BE ENTANGLED AND YET NOT VIOLATE THE CONVENTIONAL BELL INEQUALITY.

19. OTHER MEASURES CONCURRENCE TANGLE ENTROPY

20. ENTROPY ENTROPY OF ENTANGLEMENT IS A GOOD ENTANGLEMENT MEASURE FOR BIPARTITE PURE STATES. FOR A PURE STATE ρ(ab) = |ψ>< ψ| Ε(ρ(ab) ) = S(ρ(a)) = S (ρ(b)) WHERE ρ(a) = Trbρ(ab) ρ(b) = Traρ(ab) AND S IS THE VON NEUMANN ENTROPY S = - Tr (ρ ln ρ)

21. MONOGAMY OF ENTANGLEMENT IF TWO QUBITS A AND B ARE MAXIMALLY QUANTUMLY CORRELATED, THEY CANNOT BE CORRELATED AT ALL WITH A THIRD QUBIT C FOR ANY TRIPARTITE SYSTEM E(A|B1) + E(A|B2) ≤ E(A|B1B2)

22. QUANTUM TELEPORTATION • C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters (1993) BIRTH OF ALICE AND BOB ALICE CAN SEND BOB ‘QUANTUM INFORMATION’ (i.e. THE EXACT STATE OF A QUBIT) BY SHARING AN ENTANGLED STATE BETWEEN THEM AND EXCHANGING 2 BITS CLASSICAL INFORMATION.

24. QUANTUM CRYPTOGRAPHY QM GUARANTEES THAT MEASURING QUANTUM DATA DISTURBS THAT DATA, AND THIS CAN BE USED TO DETECT EAVESDROPPING IN QUANTUM KEY DISTRIBUTIONS. THIS IS DONE BY ENCODING THE INFORMATION IN NON-ORTHOGONAL STATES WHICH CANNOT BE MEASURED WITHOUT DISTURBING THE ORIGINAL STATE.

25. PROTOCOLS C H BENNETT, G BRASSARD (BB84) DEVELOPED A NEW METHOD OF SECURE QUANTUM KEY DISTRIBUTION BASED ON ‘CONJUGATE VARIABLES’ A EKERT (1990) DEVELOPED ANOTHER METHOD BY USING ENTANGLED PHOTON PAIRS VARIOUS OTHER PROTOCOLS HAVE BEEN DESIGNED AND ARE BEING PUT TO COMMERCIAL USE

26. QUANTUM KEY DISTRIBUTION NETWORKS DARPA SECOQC SWISSQUANTUM TOKYO QKD LOS ALAMOS NATIONAL LABS

27. ENTANGLEMENT IN CLASSICAL POLARIZATION OPTICS

28. AZIMUTHAL PLARIZATION

29. ENTANGLEMENT IS SOMETIMES ENOUGH NATURAL UNPOLARIZED THERMAL LIGHT IS A BELL STATE |e> = (1/√2) [ |u1> |f1> + |u2> |f2> ] : BI VIOLATION WITHOUT NONLOCALITY PARTIALLY POLARIZED LIGHT IS NOT MAXIMALLY ENTANGLED |e> = κ1 |u1> |f1> + κ2 |u2> |f2> ] FULLY POLARIZED LIGHT IS A PRODUCT STATE BI VIOLATION IS NOT A UNIQUE INDICATOR OF ENTANGLEMENT, QUANTUMNESS OR NONLOCALITY

30. BELL-LIKE INEQUALITIES ARE VIOLATED BY SUCH LIGHT R J C SPREEUW (1998) P GHOSE & M K SAMAL (2001) B N SIMON et al (2010), BORGES et al (2010), G S AGARWAL et al (2013), X-F Qian and J. H. Eberly (2013), K H KAGALWALA et al (2013) P GHOSE AND A MUKHERJEE, Rev of Theoret Sc vol. 2, pp 1-14, 2014.

31. QUANTUMNESS OTHER THAN ENTANGLEMENT? THE LEGGETT-GARG INEQUALITY(1985) MACROREALISM: A) A MACROSCOPIC OBJECT WHICH HAS AVAILABLE TO IT TWO OR MORE MACROSCOPICALLY DISTINCT STATES IS AT ANY GIVEN TIME IN A DEFINITE ONE OF THOSE STATES B) NON-INVASIVE MEASUREABILITY: IT IS POSSIBLE IN PRINCIPLE TO DETERMINE WHICH OF THESE STATES THE SYSTEM IS IN WITHOUT ANY EFFECT ON THE SYSTEM ITSELF OR ON THE SUBSEQUENT SYSTEM DYNAMICS QUANTUM SYSTEMS, NO MATTER HOW MACROSCOPIC, VIOLATE THESE POSTULATES

32. ONTOLOGICAL MODELS OF Ψ HARRIGAN AND SPEKKENS (2010) DOES THE QUANTUM STATE REPRESENT REALITY OR MERELY OUR KNOWLEDGE OF REALITY? IS REALITY LOCAL OR NONLOCAL?

33. WHAT IS AN ONTOLOGICAL MODEL? • THEORY MUST BE FORMULATED OPERATIONALLY, i.e. THE PRIMITIVES OF DESCRIPTION ARE PREPARATIONS AND MEASUREMENTS • IN AN ONTOLOGICAL MODEL OF AN OPERATIONAL THEORY THE PRIMITIVES ARE PROPERTIES OF THE MICROSCOPIC SYSTEMS

34. A PREPARATION P PREPARES A SYTEM WITH CERTAIN PROPERTIES AND A MEASUREMENT M REVEALS THOSE PROPERTIES • A COMPLETE SPECIFICATION OF THE PROPERTIES OF A SYSTEM IS CALLED AN ‘ONTIC STATE’ AND IS DENOTED BY λ • THE ONTIC STATE SPACE IS DENOTED BY Λ

35. EVEN WHEN AN OBSERVER KNOWS THE PREPARATION PROCEDURE P, SHE MAY NOT KNOW THE EXACT ONTIC STATE THAT IS PRODUCED, AND ASSIGNS OVER Λ A PROBABILITY DISTRIBUTION μ(ψ|λ) >0 AND AN ‘INDICATOR FUNCTION’ ξ (ψ|λ) TO EACH STATE ψ SUCH THAT THE BORN RULE IS REPRODUCED:

36. BORN RULE ∫ d λξ (φ|λ) μ(ψ|λ) = |< φ| ψ>|2 ∫ d λμ(ψ|λ) = 1 AN INDICATOR/RESPONSE FUNCTION IS DEFINED BY ξ (ψ|λ) = 1 FOR ALL λ IN Λψ = 0 ELSEWHERE

37. SCHEMATIC VIEWS OF THE ONTIC STATE SPACE FOR 3 MODELS

38. SCHEMATIC REPRESENTATIONS OF PROBABILITY DISTRIBUTIONS ASSOCIATED WITH ψ IN 3 MODELS

39. TWO DISTINCTIONS AND THREE CLASSES OF ONTOLOGICAL MODELS

40. THE PBR THEOREM PUSEY, BARRETT AND RUDOLPH (2012) UNDER THE REASONABLE ASSUMPTION OF PREPARATION INDEPENDENCE Ψ-EPISTEMIC MODELS ARE INCOMPATIBLE WITH STANDARD ORTHODOX QUANTUM MECHANICS

41. INFORMATION AGE IN THIS AGE OF QUANTUM INFORMATION SCIENCE Ψ IS REGARDED PRIMARILY AS MERE KNOWLEDGE. THE PBR THEOREM IS A SHOCK IN THIS RESPECT. EINSTEIN PREFERRED THE EPISTEMIC INTERPRETATION OF Ψ QUANTUM BAYESIANISM (QBISM) ADVOCATES AN EPISTEMIC INTERPRETATION Fuchs, Mermin and Schack

42. SOME INDIAN RESEARCH GROUPS IN QIP IISc BANGALORE AND IISER PUNE (NMR) HARISH-CHANDRA RESEARCH INSTITUTE, ALLAHABAD S N BOSE NATIONAL CENTRE FOR BASIC SCIENCES & BOSE INSTITUTE, KOLKATA INDIAN INSTITUTE OF MATHEMATICAL SCIENCES, CHENNAI IIT KANPUR (EXP QUANTUM OPTICS) IOP, BHUBANESWAR