44 research outputs found
Discord and quantum computational resources
Discordant states appear in a large number of quantum phenomena and seem to
be a good indicator of divergence from classicality. While there is evidence
that they are essential for a quantum algorithm to have an advantage over a
classical one, their precise role is unclear. We examine the role of discord in
quantum algorithms using the paradigmatic framework of `restricted distributed
quantum gates' and show that manipulating discordant states using local
operations has an associated cost in terms of entanglement and communication
resources. Changing discord reduces the total correlations and reversible
operations on discordant states usually require non-local resources. Discord
alone is, however, not enough to determine the need for entanglement. A more
general type of similar quantities, which we call K-discord, is introduced as a
further constraint on the kinds of operations that can be performed without
entanglement resources.Comment: Closer to published versio
Polarization rotation, reference frames and Mach's principle
Polarization of light rotates in a gravitational field. The accrued phase is
operationally meaningful only with respect to a local polarization basis. In
stationary space-times, we construct local reference frames that allow us to
isolate the Machian gravimagnetic effect from the geodetic (mass) contribution
to the rotation. The Machian effect is supplemented by the geometric term that
arises from the choice of standard polarizations. The phase accrued along a
close trajectory is gauge-independent and is zero in the Schwarzschild
space-time. The geometric term may give a dominant contribution to the phase.
We calculate polarization rotation for several trajectories and find it to be
more significant than is usually believed, pointing to its possible role as a
future gravity probe.Comment: 4 pages. Final versio
Criteria for measures of quantum correlations
Entanglement does not describe all quantum correlations and several authors
have shown the need to go beyond entanglement when dealing with mixed states.
Various different measures have sprung up in the literature, for a variety of
reasons, to describe bipartite and multipartite quantum correlations; some are
known under the collective name quantum discord. Yet, in the same sprit as the
criteria for entanglement measures, there is no general mechanism that
determines whether a measure of quantum and classical correlations is a proper
measure of correlations. This is partially due to the fact that the answer is a
bit muddy. In this article we attempt tackle this muddy topic by writing down
several criteria for a "good" measure of correlations. We breakup our list into
necessary, reasonable, and debatable conditions. We then proceed to prove
several of these conditions for generalized measures of quantum correlations.
However, not all conditions are met by all measures; we show this via several
examples. The reasonable conditions are related to continuity of correlations,
which has not been previously discussed. Continuity is an important quality if
one wants to probe quantum correlations in the laboratory. We show that most
types of quantum discord are continuous but none are continuous with respect to
the measurement basis used for optimization.Comment: 22 pages, closer to published versio
Nonlocal measurements via quantum erasure
Non-local observables play an important role in quantum theory, from Bell
inequalities and various post-selection paradoxes to quantum error correction
codes. Instantaneous measurement of these observables is known to be a
difficult problem, especially when the measurements are projective. The
standard von Neumann Hamiltonian used to model projective measurements cannot
be implemented directly in a non-local scenario and can, in some cases, violate
causality. We present a scheme for effectively generating the von Neumann
Hamiltonian for non-local observables without the need to communicate and
adapt. The protocol can be used to perform weak and strong (projective)
measurements, as well as measurements at any intermediate strength. It can also
be used in practical situations beyond non-local measurements. We show how the
protocol can be used to probe a version of Hardy's paradox with both weak and
strong measurements. The outcomes of these measurements provide a non-intuitive
picture of the pre- and post-selected system. Our results shed new light on the
interplay between quantum measurements, uncertainty, non-locality, causality
and determinism.Comment: Similar to published versio
A scheme for performing strong and weak sequential measurements of non-commuting observables
Quantum systems usually travel a multitude of different paths when evolving
through time from an initial to a final state. In general, the possible paths
will depend on the future and past boundary conditions, as well as the system's
dynamics. We present a gedanken experiment where a single system apparently
follows mutually exclusive paths simultaneously, each with probability one,
depending on which measurement was performed. This experiment involves the
measurement of observables that do not correspond to Hermitian operators. Our
main result is a scheme for measuring these operators. The scheme is based on
the erasure protocol [Phys. Rev. Lett. 116, 070404 (2016), arXiv:1409.1575] and
allows a wide range of sequential measurements at both the weak and strong
limits. At the weak limit the back action of the measurement cannot be used to
account for the surprising behavior and the resulting weak values provide a
consistent yet strange account of the system's past.Comment: Similar to published version, Quantum Studies: Mathematics and
Foundations (2016). arXiv admin note: text overlap with arXiv:1409.157