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Our goal is to compare two unequivalent definitions of the Gell-Mann

channels. It turns out that both definitions coincide for qubits and qutrits.

In higher dimensions, there exist some constraints under which the channels

describe the same dynamics. Finally, we find the GKSL time-local generators for

a class of the Gell-Mann channels.

A qudit code is a subspace of the state space of a fixed number of qudits.

Such a code is permutation-invariant if it is unchanged under the swapping of

any pair of the underlying qudits. Prior permutation-invariant codes encode a

single qubit into $N$ qubits that correct $t$ arbitrary errors. We design

permutation-invariant codes encoding a $d$-level system into $N$ qudits that

correct $t$ arbitrary errors. The logical codewords in our

permutation-invariant qudits codes are linear combinations of Dicke states,

The coherent control of spin qubits forms the basis of many applications in

quantum information processing and nanoscale sensing, imaging and spectroscopy.

Such control is conventionally achieved by direct driving of the qubit

transition with a resonant global field, typically at microwave frequencies.

Here we introduce an approach that relies on the resonant driving of nearby

environment spins, whose localised magnetic field in turn drives the qubit when

We provide a scheme for inferring causal relations from uncontrolled

statistical data based on tools from computational algebraic geometry, in

particular, the computation of Groebner bases. We focus on causal structures

containing just two observed variables, each of which is binary. We consider

the consequences of imposing different restrictions on the number and

cardinality of latent variables and of assuming different functional

dependences of the observed variables on the latent ones (in particular, the

The transport of sound and heat, in the form of phonons, can be limited by

disorder-induced scattering. In electronic and optical settings the

introduction of chiral transport, in which carrier propagation exhibits parity

asymmetry, can remove elastic backscattering making carrier transport robust

against unwanted disorder. While chiral transport is also achievable for

phonons the suppression of disorder-induced scattering has never been

demonstrated in non-topological phononic systems. Here we experimentally

Here we show that, if we insert context dependent unitary evolutions (which

can be achieved via post selection) into spatial (i.e., normal) Bell-CHSH test,

then it is possible to violate space-time Bell-CHSH inequality maximally (i.e.,

up to $4$). However this does not contradict Tsirelson quantum bound

($2\sqrt{2}$), as the latter has been derived without taking into consideration

context dependent unitary evolutions and/or post selection. As an important

We demonstrate that temporal observables, which are sensitive to a system's

history (as opposed to its state), implicate entangled histories. We exemplify

protocols for measuring such observables, and algorithms for predicting the

(stochastic) outcomes of such measurements. Temporal observables allow us to

define, and potentially to measure, precise mathematical consequences of

intrinsically disjoint, yet mutually accessible, branches within the evolution

of a pure quantum state.

We consider a family of quantum channels characterized by the fact that

certain (in general nonorthogonal) Pure states at the channel entrance are

mapped to (tensor) Products of Pure states (PPP, hence "pcubed") at the

complementary outputs (the main output and the "environment") of the channel.

The pcubed construction, a reformulation of the twisted-diagonal procedure by

M. M Wolf and D. Perez-Garcia, [Phys. Rev. A 75, 012303 (2007)], can be used to

produce a large class of degradable quantum channels; degradable channels are

Instantaneous quantum computing is a sub-universal quantum complexity class,

whose circuits have proven to be hard to simulate classically in the

Discrete-Variable (DV) realm. We extend this proof to the Continuous-Variable

(CV) domain by using squeezed states and homodyne detection, and by exploring

the properties of post-selected circuits. In order to treat post-selection in

CVs we consider finitely-resolved homodyne detectors, corresponding to a

realistic scheme based on discrete probability distributions of the measurement

In the early days of quantum mechanics, it was believed that the time energy

uncertainty principle (TEUP) bounds the efficiency of energy measurements,

relating the duration ($\Delta t$) of the measurement, and its accuracy error

($\Delta E$) by $\Delta t\Delta E \ge$ 1/2. In 1961 Y. Aharonov and Bohm gave a

counterexample, whereas Aharonov, Massar and Popescu [2002] showed that under

certain conditions the principle holds. Can we classify when and to what extent

the TEUP is violated?