7,950 research outputs found
Quantum Reality and Measurement: A Quantum Logical Approach
The recently established universal uncertainty principle revealed that two
nowhere commuting observables can be measured simultaneously in some state,
whereas they have no joint probability distribution in any state. Thus, one
measuring apparatus can simultaneously measure two observables that have no
simultaneous reality. In order to reconcile this discrepancy, an approach based
on quantum logic is proposed to establish the relation between quantum reality
and measurement. We provide a language speaking of values of observables
independent of measurement based on quantum logic and we construct in this
language the state-dependent notions of joint determinateness, value identity,
and simultaneous measurability. This naturally provides a contextual
interpretation, in which we can safely claim such a statement that one
measuring apparatus measures one observable in one context and simultaneously
it measures another nowhere commuting observable in another incompatible
context.Comment: 16 pages, Latex. Presented at the Conference "Quantum Theory:
Reconsideration of Foundations, 5 (QTRF5)," Vaxjo, Sweden, 15 June 2009. To
appear in Foundations of Physics
Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
The Heisenberg uncertainty principle states that the product of the noise in
a position measurement and the momentum disturbance caused by that measurement
should be no less than the limit set by Planck's constant, hbar/2, as
demonstrated by Heisenberg's thought experiment using a gamma-ray microscope.
Here I show that this common assumption is false: a universally valid trade-off
relation between the noise and the disturbance has an additional correlation
term, which is redundant when the intervention brought by the measurement is
independent of the measured object, but which allows the noise-disturbance
product much below Planck's constant when the intervention is dependent. A
model of measuring interaction with dependent intervention shows that
Heisenberg's lower bound for the noise-disturbance product is violated even by
a nearly nondisturbing, precise position measuring instrument. An experimental
implementation is also proposed to realize the above model in the context of
optical quadrature measurement with currently available linear optical devices.Comment: Revtex, 6 page
Minimum-energy pulses for quantum logic cannot be shared
We show that if an electromagnetic energy pulse with average photon number
is used to carry out the same quantum logical operation on a set of N
atoms, either simultaneously or sequentially, the overall error probability in
the worst case scenario (i.e., maximized over all the possible initial atomic
states) scales as N^2/. This means that in order to keep the error
probability bounded by N\epsilon, with \epsilon ~ 1/, one needs to use
N/\epsilon photons, or equivalently N separate "minimum-energy'' pulses: in
this sense the pulses cannot, in general, be shared. The origin for this
phenomenon is found in atom-field entanglement. These results may have
important consequences for quantum logic and, in particular, for large-scale
quantum computation.Comment: To appear in Phys. Rev. A, Rapid Communication
Quantum Limits of Measurements Induced by Multiplicative Conservation Laws: Extension of the Wigner-Araki-Yanase Theorem
The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws
limit the accuracy of measurements. Recently, various quantitative expressions
have been found for quantum limits on measurements induced by additive
conservation laws, and have been applied to the study of fundamental limits on
quantum information processing. Here, we investigate generalizations of the WAY
theorem to multiplicative conservation laws. The WAY theorem is extended to
show that an observable not commuting with the modulus of, or equivalently the
square of, a multiplicatively conserved quantity cannot be precisely measured.
We also obtain a lower bound for the mean-square noise of a measurement in the
presence of a multiplicatively conserved quantity. To overcome this noise it is
necessary to make large the coefficient of variation (the so-called relative
fluctuation), instead of the variance as is the case for additive conservation
laws, of the conserved quantity in the apparatus.Comment: 8 pages, REVTEX; typo added, to appear in PR
Gate fidelity of arbitrary single-qubit gates constrained by conservation laws
Recent investigations show that conservation laws limit the accuracy of gate
operations in quantum computing. The inevitable error under the angular
momentum conservation law has been evaluated so far for the CNOT, Hadamard, and
NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we
extend the above results to general single-qubit gates. We obtain an upper
bound of the gate fidelity of arbitrary single-qubit gates implemented under
arbitrary conservation laws, determined by the geometry of the conservation law
and the gate operation on the Bloch sphere as well as the size of the ancilla.Comment: Title changed; to appear in J. Phys. A: Math. Theor.; 19 pages, 2
figure
Instruments and channels in quantum information theory
While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
typical inequalities for the quantum and classical relative entropies, many
bounds on the classical information extracted in a quantum measurement, of the
type of Holevo's bound, are obtained in a unified manner.Comment: 12 pages, revtex
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