QUANTUM MECHANICS AND
QUANTUM INFORMATION SCIENCE
WHAT IS Ψ?
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IS Ψ ONTIC OR EPISTEMIC?
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WHAT IS A QUANTUM MEASUREMENT?
QUANTUM PARADOXES
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THE DOUBLE-SLIT: WAVE-PARTICLE DUALITY
(1905-1927-)
SCHRöDINGER CAT (1035)
EPR PARADOX AND QUANTUM
ENTANGLEMENT (1935)
INTERPRETATIONS
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BOHR VS VON NEUMANN/DIRAC
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EVERETT (MANY WORLDS?) (1957-)
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HIDDEN VARIABLES (1935-)
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OTHERS (MODAL, CONSISTENT HISTORIES,
ETC)
NO-GO THEOREMS FOR HIDDEN
VARIABLES
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VON NEUMANN THEOREM (1932)
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BELL’S THEOREM (1964)
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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
=¼
THIS CONTRADICTS THE STANDARD QM
PREDICTION
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
BREAKTHROUGH
QUANTUM 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
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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
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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 KEY
DISTRIBUTIONS. THIS IS DONE BY ENCODING THE
INFORMATION IN NON-ORTHOGONAL STATES WHICH
CANNOT BE MEASURED WITHOUT DISTURBING THE
ORIGINAL 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?
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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
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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 INTERPRETATION
Fuchs, 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