53,648 research outputs found
Scrambling as verum focus: German scrambling meets Romance anaphoric anteposition.
In this paper I demonstrate that in Mòcheno, a German dialect spoken in Northern Italy,
scrambling, i.e. the movement of any constituent above sentential adverbs and below the finite verb,
is permitted like in Continental Germanic languages. Unlike in these languages, however, leftward
movement is not triggered by specificity or scope-fixing (A-scrambling) or by the need to check
any topic or contrastive/new-information focus discourse-features (A’-scrambling). By relying on
information structure, the syntax of modal particles and the distribution of scrambling in sentences
with fronted operators, I provide evidence that scrambling in Mòcheno triggers a verum focus reading
on the truth value of the sentence and involves a type of focus movement to a FocusP in CP. That
scrambling can be associated with verum focus is a unicum among Continental Germanic languages,
which I show follows from a reanalyis of the properties of Germanic focus scrambling under the
influence of Romance anaphoric anteposition
Entropic uncertainty relations for quantum information scrambling
How violently do two quantum operators disagree? Different fields of physics
feature different measures of incompatibility: (i) In quantum information
theory, entropic uncertainty relations constrain measurement outcomes. (ii) In
condensed matter and high-energy physics, the out-of-time-ordered correlator
(OTOC) signals scrambling, the spread of information through many-body
entanglement. We unite these measures, proving entropic uncertainty relations
for scrambling. The entropies are of distributions over weak and strong
measurements' possible outcomes. The weak measurements ensure that the OTOC
quasiprobability (a nonclassical generalization of a probability, which
coarse-grains to the OTOC) governs terms in the uncertainty bound. The
quasiprobability causes scrambling to strengthen the bound in numerical
simulations of a spin chain. This strengthening shows that entropic uncertainty
relations can reflect the type of operator disagreement behind scrambling.
Generalizing beyond scrambling, we prove entropic uncertainty relations
satisfied by commonly performed weak-measurement experiments. We unveil a
physical significance of weak values (conditioned expectation values): as
governing terms in entropic uncertainty bounds.Comment: Close to published version, but has more-pedagogical formatting. 13
pages, including 4 figure
Scrambling speed of random quantum circuits
Random transformations are typically good at "scrambling" information.
Specifically, in the quantum setting, scrambling usually refers to the process
of mapping most initial pure product states under a unitary transformation to
states which are macroscopically entangled, in the sense of being close to
completely mixed on most subsystems containing a fraction fn of all n particles
for some constant f. While the term scrambling is used in the context of the
black hole information paradox, scrambling is related to problems involving
decoupling in general, and to the question of how large isolated many-body
systems reach local thermal equilibrium under their own unitary dynamics.
Here, we study the speed at which various notions of scrambling/decoupling
occur in a simplified but natural model of random two-particle interactions:
random quantum circuits. For a circuit representing the dynamics generated by a
local Hamiltonian, the depth of the circuit corresponds to time. Thus, we
consider the depth of these circuits and we are typically interested in what
can be done in a depth that is sublinear or even logarithmic in the size of the
system. We resolve an outstanding conjecture raised in the context of the black
hole information paradox with respect to the depth at which a typical quantum
circuit generates an entanglement assisted encoding against the erasure
channel. In addition, we prove that typical quantum circuits of poly(log n)
depth satisfy a stronger notion of scrambling and can be used to encode alpha n
qubits into n qubits so that up to beta n errors can be corrected, for some
constants alpha, beta > 0.Comment: 24 pages, 2 figures. Superseded by http://arxiv.org/abs/1307.063
Information Scrambling in Quantum Neural Networks
The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks
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