1,139 research outputs found
Shadow Tomography of Quantum States
We introduce the problem of *shadow tomography*: given an unknown
-dimensional quantum mixed state , as well as known two-outcome
measurements , estimate the probability that
accepts , to within additive error , for each of the
measurements. How many copies of are needed to achieve this, with high
probability? Surprisingly, we give a procedure that solves the problem by
measuring only copies. This means, for example, that we can learn the behavior of an
arbitrary -qubit state, on all accepting/rejecting circuits of some fixed
polynomial size, by measuring only copies of the state.
This resolves an open problem of the author, which arose from his work on
private-key quantum money schemes, but which also has applications to quantum
copy-protected software, quantum advice, and quantum one-way communication.
Recently, building on this work, Brand\~ao et al. have given a different
approach to shadow tomography using semidefinite programming, which achieves a
savings in computation time.Comment: 29 pages, extended abstract appeared in Proceedings of STOC'2018,
revised to give slightly better upper bound (1/eps^4 rather than 1/eps^5) and
lower bounds with explicit dependence on the dimension
On the capacities of bipartite Hamiltonians and unitary gates
We consider interactions as bidirectional channels. We investigate the
capacities for interaction Hamiltonians and nonlocal unitary gates to generate
entanglement and transmit classical information. We give analytic expressions
for the entanglement generating capacity and entanglement-assisted one-way
classical communication capacity of interactions, and show that these
quantities are additive, so that the asymptotic capacities equal the
corresponding 1-shot capacities. We give general bounds on other capacities,
discuss some examples, and conclude with some open questions.Comment: V3: extensively rewritten. V4: a mistaken reference to a conjecture
by Kraus and Cirac [quant-ph/0011050] removed and a mistake in the order of
authors in Ref. [53] correcte
Entanglement can completely defeat quantum noise
We describe two quantum channels that individually cannot send any
information, even classical, without some chance of decoding error. But
together a single use of each channel can send quantum information perfectly
reliably. This proves that the zero-error classical capacity exhibits
superactivation, the extreme form of the superadditivity phenomenon in which
entangled inputs allow communication over zero capacity channels. But our
result is stronger still, as it even allows zero-error quantum communication
when the two channels are combined. Thus our result shows a new remarkable way
in which entanglement across two systems can be used to resist noise, in this
case perfectly. We also show a new form of superactivation by entanglement
shared between sender and receiver.Comment: 4 pages, 1 figur
Allopurinol use yields potentially beneficial effects on inflammatory indices in those with recent ischemic stroke: a randomized, double-blind, placebo-controlled trial
<p><b>Background and Purpose</b>: Elevated serum uric acid level is associated with poor outcome and increased risk of recurrent events after stroke. The xanthine oxidase inhibitor allopurinol lowers uric acid but also attenuates expression of inflammatory adhesion molecules in murine models, reduces oxidative stress in the vasculature, and improves endothelial function. We sought to investigate whether allopurinol alters expression of inflammatory markers after acute ischemic stroke.</p>
<p><b>Methods</b>: We performed a randomized, double-blind, placebo-controlled trial to investigate the safety, tolerability, and effect of 6 weeks’ treatment with high- (300 mg once a day) or low- (100 mg once a day) dose allopurinol on levels of uric acid and circulating inflammatory markers after ischemic stroke.</p>
<p><b>Results</b>: We enrolled 50 patients with acute ischemic stroke (17, 17, and 16 in the high, low, and placebo groups, respectively). Mean (±SD) age was 70 (±13) years. Groups had similar characteristics at baseline. There were no serious adverse events. Uric acid levels were significantly reduced at both 7 days and 6 weeks in the high-dose group (by 0.14 mmol/L at 6 weeks, P=0.002). Intercellular adhesion molecule-1 concentration (ng/mL) rose by 51.2 in the placebo group, rose slightly (by 10.6) in the low-dose allopurinol group, but fell in the high-dose group (by 2.6; difference between groups P=0.012, Kruskal-Wallis test).</p>
<p><b>Conclusion</b>: Allopurinol treatment is well tolerated and attenuates the rise in intercellular adhesion molecule-1 levels seen after stroke. Uric acid levels were lowered with high doses. These findings support further evaluation of allopurinol as a preventive measure after stroke.</p>
Symmetric coupling of four spin-1/2 systems
We address the non-binary coupling of identical angular momenta based upon
the representation theory for the symmetric group. A correspondence is pointed
out between the complete set of commuting operators and the
reference-frame-free subsystems. We provide a detailed analysis of the coupling
of three and four spin-1/2 systems and discuss a symmetric coupling of four
spin-1/2 systems.Comment: 20 pages, no figure
The cryptographic power of misaligned reference frames
Suppose that Alice and Bob define their coordinate axes differently, and the
change of reference frame between them is given by a probability distribution
mu over SO(3). We show that this uncertainty of reference frame is of no use
for bit commitment when mu is uniformly distributed over a (sub)group of SO(3),
but other choices of mu can give rise to a partially or even asymptotically
secure bit commitment.Comment: 4 pages Latex; v2 has a new referenc
Modelling the Longitudinal Dynamics of Paranoia in Psychosis:A Temporal Network Analysis Over 20 Years
Paranoia is a highly debilitating, core element of psychosis, although is poorly managed. Theories of paranoia mostly interface with short-scale or cross-sectional data models, leaving the longitudinal course of paranoia underspecified. Here, we develop an empirical characterisation of two aspects of paranoia - persecutory and referential delusions - in individuals with psychosis over 20 years. We examine delusional dynamics by applying a Graphical Vector Autoregression Model to data collected from the Chicago Follow-up Study. We adjusted for age, sex, IQ, and antipsychotic use. We found that referential and persecutory delusions are central themes, supported by other primary delusions, and are strongly autoregressive. In a second analysis we demonstrate that social factors influence the severity of referential, but not persecutory, delusions. We suggest that persecutory delusions represent central, resistant states in the cognitive landscape, whereas referential beliefs are more flexible, offering an important window of opportunity for intervention. Our data models can be collated with prior biological, computational, and social work to contribute toward a more complete theory of paranoia and provide more time-dependent evidence for optimal treatment targets
Randomized benchmarking of single and multi-qubit control in liquid-state NMR quantum information processing
Being able to quantify the level of coherent control in a proposed device
implementing a quantum information processor (QIP) is an important task for
both comparing different devices and assessing a device's prospects with
regards to achieving fault-tolerant quantum control. We implement in a
liquid-state nuclear magnetic resonance QIP the randomized benchmarking
protocol presented by Knill et al (PRA 77: 012307 (2008)). We report an error
per randomized pulse of with a
single qubit QIP and show an experimentally relevant error model where the
randomized benchmarking gives a signature fidelity decay which is not possible
to interpret as a single error per gate. We explore and experimentally
investigate multi-qubit extensions of this protocol and report an average error
rate for one and two qubit gates of for a three
qubit QIP. We estimate that these error rates are still not decoherence limited
and thus can be improved with modifications to the control hardware and
software.Comment: 10 pages, 6 figures, submitted versio
Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
The Schur basis on n d-dimensional quantum systems is a generalization of the
total angular momentum basis that is useful for exploiting symmetry under
permutations or collective unitary rotations. We present efficient (size
poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur
transform, which is the change of basis between the computational and the Schur
bases. These circuits are based on efficient circuits for the Clebsch-Gordan
transformation. We also present an efficient circuit for a limited version of
the Schur transform in which one needs only to project onto different Schur
subspaces. This second circuit is based on a generalization of phase estimation
to any nonabelian finite group for which there exists a fast quantum Fourier
transform.Comment: 4 pages, 3 figure
How to hide a secret direction
We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur
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