16,096 research outputs found
Error Analysis For Encoding A Qubit In An Oscillator
In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev,
and Preskill [quant-ph/0008040] described a method to encode a qubit in the
continuous Hilbert space of an oscillator's position and momentum variables.
This encoding provides a natural error correction scheme that can correct
errors due to small shifts of the position or momentum wave functions (i.e.,
use of the displacement operator). We present bounds on the size of correctable
shift errors when both qubit and ancilla states may contain errors. We then use
these bounds to constrain the quality of input qubit and ancilla states.Comment: 5 pages, 8 figures, submitted to Physical Review
Contextuality under weak assumptions
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term "probabilistic contextuality", drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a "possibilistic" analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known "no-go" theorems that constrain ψ-epistemic models for quantum mechanics
Can lay-led walking programmes increase physical activity in middle aged adults? : a randomised controlled trial
Study objective: To compare health walks, a community based lay-led walking scheme versus advice
only on physical activity and cardiovascular health status in middle aged adults.
Design: Randomised controlled trial with one year follow up. Physical activity was measured by questionnaire.
Other measures included attitudes to exercise, body mass index, cholesterol, aerobic capacity,
and blood pressure.
Setting: Primary care and community.
Participants: 260 men and women aged 40–70 years, taking less than 120 minutes of moderate
intensity activity per week.
Main results: Seventy three per cent of people completed the trial. Of these, the proportion increasing
their activity above 120 minutes of moderate intensity activity per week was 22.6% in the advice only
and 35.7% in the health walks group at 12 months (between group difference =13% (95% CI 0.003%
to 25.9%) p=0.05). Intention to treat analysis, using the last known value for missing cases,
demonstrated smaller differences between the groups (between group difference =6% (95% CI -5% to
16.4%)) with the trend in favour of health walks. There were improvements in the total time spent and
number of occasions of moderate intensity activity, and aerobic capacity, but no statistically significant
differences between the groups. Other cardiovascular risk factors remained unchanged.
Conclusions: There were no significant between group differences in self reported physical activity at
12 month follow up when the analysis was by intention to treat. In people who completed the trial,
health walks was more effective than giving advice only in increasing moderate intensity activity above
120 minutes per week
Degradation of a quantum directional reference frame as a random walk
We investigate if the degradation of a quantum directional reference frame
through repeated use can be modeled as a classical direction undergoing a
random walk on a sphere. We demonstrate that the behaviour of the fidelity for
a degrading quantum directional reference frame, defined as the average
probability of correctly determining the orientation of a test system, can be
fit precisely using such a model. Physically, the mechanism for the random walk
is the uncontrollable back-action on the reference frame due to its use in a
measurement of the direction of another system. However, we find that the
magnitude of the step size of this random walk is not given by our classical
model and must be determined from the full quantum description.Comment: 5 pages, no figures. Comments are welcome. v2: several changes to
clarify the key results. v3: journal reference added, acknowledgements and
references update
Relativistically invariant quantum information
We show that quantum information can be encoded into entangled states of
multiple indistinguishable particles in such a way that any inertial observer
can prepare, manipulate, or measure the encoded state independent of their
Lorentz reference frame. Such relativistically invariant quantum information is
free of the difficulties associated with encoding into spin or other degrees of
freedom in a relativistic context.Comment: 5 pages, published versio
Optimal measurements for relative quantum information
We provide optimal measurement schemes for estimating relative parameters of
the quantum state of a pair of spin systems. We prove that the optimal
measurements are joint measurements on the pair of systems, meaning that they
cannot be achieved by local operations and classical communication. We also
demonstrate that in the limit where one of the spins becomes macroscopic, our
results reproduce those that are obtained by treating that spin as a classical
reference direction.Comment: 6 pages, 1 figure, published versio
Observers can always generate nonlocal correlations without aligning measurements by covering all their bases
Quantum theory allows for correlations between the outcomes of distant
measurements that are inconsistent with any locally causal theory, as
demonstrated by the violation of a Bell inequality. Typical demonstrations of
these correlations require careful alignment between the measurements, which
requires distant parties to share a reference frame. Here, we prove, following
a numerical observation by Shadbolt et al., that if two parties share a Bell
state and each party randomly chooses three orthogonal measurements, then the
parties will always violate a Bell inequality. Furthermore, we prove that this
probability is highly robust against local depolarizing noise, in that small
levels of noise only decrease the probability of violating a Bell inequality by
a small amount. We also show that generalizing to N parties increases the
robustness against noise. These results improve on previous ones that only
allowed a high probability of violating a Bell inequality for large numbers of
parties.Comment: 4 pages, 2 figures. v2: updated reference. v3: published versio
Preparation and manipulation of a fault-tolerant superconducting qubit
We describe a qubit encoded in continuous quantum variables of an rf
superconducting quantum interference device. Since the number of accessible
states in the system is infinite, we may protect its two-dimensional subspace
from small errors introduced by the interaction with the environment and during
manipulations. We show how to prepare the fault-tolerant state and manipulate
the system. The discussed operations suffice to perform quantum computation on
the encoded state, syndrome extraction, and quantum error correction. We also
comment on the physical sources of errors and possible imperfections while
manipulating the system.Comment: Typo corrected, title changed as suggested by the editors of Phys.
Rev. B, references adde
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