Instantaneous measurements of nonlocal variables Stateoperator and teleportation approach

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Instantaneous measurements of nonlocal
variablesState-operator and teleportationapproa
ch

• Berry Groisman, Benni Reznik, Yakir Aharonov and
  Lev Vaidman
• School of Physics and Astronomy, Tel Aviv
• University, Tel Aviv 69978, Israel

We have reconsidered the measurability problem
for nonlocal operators which have been previously
considered to be in conflict with relativistic
causality and hence unmeasurable. We argue that
by weakening the preparation role of ideal
measurements, all Hermitian observables become
measurable.
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Which nonlocal variables can be measured?

before yesterday
L. Landau, and R. Peierls, Z. Phys. 69, 56
(1931)
Bell operator, AB, (AB)mod a
Y. Aharonov, D. Albert and L. Vaidman Phys. Rev.
D 34, 1805 (1986)
Today
All nonlocal variables are measurable
instantaneously!
Demolition (non-repeatable) measurement
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NONLOCAL VARIABLES
t?t-
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Instantaneous measurement
c?tltltL
Stage III Interpretation of local outcomes
IB
Stage II Local interactions, measurements and
classical recording of local outcomes
local outcomes
t0?t
t0
Stage I Preparation of measurement devices
L
Space-like regions
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A measurement of an observable prepare
eigenstate of that same observable.
1. Nondemolition measurement
Measurable
Bell (maximally entangled) eigenstates
Unmeasurable
nonlocality without entanglement
non-maximally entangled eigenstates
Bennett C H, DiVincenzo D P, Fuchs C A, Mor T,
Rains E, Shor P W, Smolin J A and Wootters W K,
(1999).
B. Groisman and L. Vaidman (2001)
J. Walgate, L. Hardy (2002)
4x4 twisted basis
S. Popescu and L. Vaidman (1994)
D. Beckman, D. Gottesman, M.A. Nielsen and J.
Preskill (2001)
A measurement of an observable does not
necessarily prepare eigenstates of that same
observable.
2. Demolition measurement
All nonlocal variables are measurable !
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How does it work?
Instantaneous demolition measurement c?tltltL
The result of nonlocal measurement
t1
IB
local outcomes
Step II Trivial local measurements
Step I instantaneous transformation of
original nonmeasurable set of eigenstates to
measurable set
Classical information is splite between A and B
t0
L
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Stator approach
2 x2 twisted product basis
Step II Bob performs a trivial measurement in
z-basis
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General2 x2 twisted product basis
More complicated, because
probability 1/2
probability 1/2
Need to be corrected
J. I. Cirac, W. D?r, B. Kraus and M.
Lewenstein, Phys. Rev. Lett, 86, 544 (2001).
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Teleportation
Step I
Step II
if Alice measures teleported
particle in z-basis
z
if Alice measures teleported
particle in x-basis
z
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BELL M-T
Additional partial teleportation with respect to
the axis
BELL M-T
Probability of success goes as
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HOW TO MEASURE GENERAL TWO-PART VARIABLE USING
TELEPORTATION?
BELL M-T i
i ?1
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Referencees

• Berry Groisman and Benni Reznik, Measurements of
  semi-local and non-maximally entangled states,
  quant-ph/0111012
• to be published in Phys. Rev. A.
• Lev Vaidman, Instantaneous measurement of
  non-local variables is possible, quant-ph/0111124.