Energy-Constrained Discrimination of Unitaries, Quantum Speed Limits, and a Gaussian Solovay-Kitaev Theorem.

We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. First, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Second, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Third, we establish a version of the Solovay-Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.

Convergence Rates for the Quantum Central Limit Theorem.

Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It implies that the state in any single output arm of an n-splitter, which is fed with n copies of a centred state ρ with finite second moments, converges to the Gaussian state with the same first and second moments as ρ . Here we exploit the phase space formalism to carry out a refined analysis of the rate of convergence in this quantum central limit theorem. For instance, we prove that the convergence takes place at a rate O n - 1 / 2 in the Hilbert-Schmidt norm whenever the third moments of ρ are finite. Trace norm or relative entropy bounds can be obtained by leveraging the energy boundedness of the state. Via analytical and numerical examples we show that our results are tight in many respects. An extension of our proof techniques to the non-i.i.d. setting is used to analyse a new model of a lossy optical fibre, where a given m-mode state enters a cascade of n beam splitters of equal transmissivities λ 1 / n fed with an arbitrary (but fixed) environment state. Assuming that the latter has finite third moments, and ignoring unitaries, we show that the effective channel converges in diamond norm to a simple thermal attenuator, with a rate O ( n - 1 2 ( m + 1 ) ) . This allows us to establish bounds on the classical and quantum capacities of the cascade channel. Along the way, we derive several results that may be of independent interest. For example, we prove that any quantum characteristic function χ ρ is uniformly bounded by some η ρ < 1 outside of any neighbourhood of the origin; also, η ρ can be made to depend only on the energy of the state ρ .

Pathophysiology, Classification and Comorbidities after Traumatic Spinal Cord Injury.

The spinal cord is a conduit within the central nervous system (CNS) that provides ongoing communication between the brain and the rest of the body, conveying complex sensory and motor information necessary for safety, movement, reflexes, and optimization of autonomic function. After a spinal cord injury (SCI), supraspinal influences on the spinal segmental control system and autonomic nervous system (ANS) are disrupted, leading to spastic paralysis, pain and dysesthesia, sympathetic blunting and parasympathetic dominance resulting in cardiac dysrhythmias, systemic hypotension, bronchoconstriction, copious respiratory secretions and uncontrolled bowel, bladder, and sexual dysfunction. This article outlines the pathophysiology of traumatic SCI, current and emerging methods of classification, and its influence on sensory/motor function, and introduces the probable comorbidities associated with SCI that will be discussed in more detail in the accompanying manuscripts of this special issue.

Entanglement cost in practical scenarios.

We quantify the one-shot entanglement cost of an arbitrary bipartite state, that is, the minimum number of singlets needed by two distant parties to create a single copy of the state up to a finite accuracy, by using local operations and classical communication only. This analysis, in contrast to the traditional one, pertains to scenarios of practical relevance, in which resources are finite and transformations can be achieved only approximately. Moreover, it unveils a fundamental relation between two well-known entanglement measures, namely, the Schmidt number and the entanglement of formation. Using this relation, we are able to recover the usual expression of the entanglement cost as a special case.

Mirror inversion of quantum states in linear registers.

Transfer of data in linear quantum registers can be significantly simplified with preengineered but not dynamically controlled interqubit couplings. We show how to implement a mirror inversion of the state of the register in each excitation subspace with respect to the center of the register. Our construction is especially appealing as it requires no dynamical control over individual interqubit interactions. If, however, individual control of the interactions is available then the mirror inversion operation can be performed on any substring of qubits in the register. In this case, a sequence of mirror inversions can generate any permutation of a quantum state of the involved qubits.

Perfect state transfer in quantum spin networks.

We propose a class of qubit networks that admit the perfect state transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2log3N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits, then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.