QUANTUM MECHANICS AND QUANTUM INFORMATION SCIENCE

WHAT IS Ψ?

IS Ψ ONTIC OR EPISTEMIC?

WHAT IS A QUANTUM MEASUREMENT?

QUANTUM PARADOXES

THE DOUBLE-SLIT: WAVE-PARTICLE DUALITY (1905-1927-)

SCHRöDINGER CAT (1035)

EPR PARADOX AND QUANTUM ENTANGLEMENT (1935)

INTERPRETATIONS

BOHR VS VON NEUMANN/DIRAC

EVERETT (MANY WORLDS?) (1957-)

HIDDEN VARIABLES (1935-)

OTHERS (MODAL, CONSISTENT HISTORIES, ETC)

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

BELL’S THEOREM

STANDARD OR ORTHODOX QUANTUM MECHANICS IS INCOMPATIBLE WITH

LOCAL REALISM

(USES LOCAL HIDDEN VARIABLES)

EINSTEIN’S 1927 ARGUMENT USES A SINGLE PARTICLE

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 = ¼THIS CONTRADICTS THE STANDARD QMPREDICTION

p(1a Λ 1b |ψ) = 0

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.

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

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

OTHER ALGORITHMS FOR

QUANTUM FOURIER TRANSFORM

QUANTUM GATES

QUANTUM ADIABATIC

QUANTUM ERROR CORRECTION

NO-CLONING THEOREM

WOOTERS, ZUREK, DIEKS (1982)

QUANTUM MECHANICS FORBIDS THE CREATION OF IDENTICAL COPIES OF AN UNKNOWN QUANTUM STATE

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

QUANTUM INFORMATION PROCESSING SCIENCE

QUANTUM COMPUTING QUANTUM COMPLEXITY THEORY QUANTUM CRYPTOGRAPHY QUANTUM ERROR CORRECTION QUANTUM COMMUNICATION

COMPLEXITY QUANTUM ENTANGLEMENT QUANTUM DENSE CODING

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

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

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.

OTHER MEASURES

CONCURRENCE

TANGLE

ENTROPY

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) = Trb ρ(ab) ρ(b) = Tra ρ(ab)

AND S IS THE VON NEUMANN ENTROPY

S = - Tr (ρ ln ρ)

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)

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.

QUANTUM CRYPTOGRAPHY

QM GUARANTEES THAT MEASURING QUANTUM DATA DISTURBS THAT DATA, AND THIS CAN BE

USED TO DETECT EAVESDROPPING IN QUANTUM KEYDISTRIBUTIONS. THIS IS DONE BY ENCODING THEINFORMATION IN NON-ORTHOGONAL STATES WHICHCANNOT BE MEASURED WITHOUT DISTURBING THEORIGINAL STATE.

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

QUANTUM KEY DISTRIBUTION NETWORKS

DARPA

SECOQC

SWISSQUANTUM

TOKYO QKD

LOS ALAMOS NATIONAL LABS

ENTANGLEMENT IN CLASSICAL POLARIZATION OPTICS

AZIMUTHAL PLARIZATION

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

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.

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

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?

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

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

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:

BORN RULE

∫ d λ ξ (φ|λ) μ(ψ|λ) = |< φ| ψ>|2

∫ d λ μ(ψ|λ) = 1

AN INDICATOR/RESPONSE FUNCTION IS DEFINED BY

ξ (ψ|λ) = 1 FOR ALL λ IN Λψ

= 0 ELSEWHERE

SCHEMATIC VIEWS OF THE ONTIC STATE SPACE FOR 3 MODELS

SCHEMATIC REPRESENTATIONS OF PROBABILITY DISTRIBUTIONS ASSOCIATED WITH ψ IN 3 MODELS

TWO DISTINCTIONS AND THREE CLASSES OF ONTOLOGICAL MODELS

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

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 INTERPRETATIONFuchs, Mermin and Schack

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