Spin chains and channels with memory

In most studies of the channel capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error. This work has led to speculation that interesting non-analytic behaviour may occur in the capacity. Motivated by these observations, we connect the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables us the techniques of many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error. The models can display analogous behaviour to associated many-body systems, including `phase transitions'.Comment: V2: changes in presentation, some additional comments on generalisation. V3: In accordance with published version, most (but not all) details of proofs now included. A separate paper will shortly be submitted separately with all details and more result

On the Origin of Metallicity and Stability of the Metastable Phase in Chemically Exfoliated MoS2_2

Chemical exfoliation of MoS$_2$ via Li-intercalation route has led to many desirable properties and spectacular applications due to the presence of a metastable state in addition to the stable H phase. However, the nature of the specific metastable phase formed, and its basic charge conduction properties have remained controversial. Using spatially resolved Raman spectroscopy (~1 micrometer resolution) and photoelectron spectroscopy (~120 nm resolution), we probe such chemically exfoliated MoS$_2$ samples in comparison to a mechanically exfoliated H phase sample and confirm that the dominant metastable state formed by this approach is a distorted T' state with a small semiconducting gap. Investigating two such samples with different extents of Li residues present, we establish that Li+ ions, not only help to exfoliate MoS$_2$ into few layer samples, but also contribute to enhancing the relative stability of the metastable state as well as dope the system with electrons, giving rise to a lightly doped small bandgap system with the T' structure, responsible for its spectacular properties.Comment: 34 pages, Main manuscript + Supplementary Materia

Experimental reversion of the optimal quantum cloning and flipping processes

The quantum cloner machine maps an unknown arbitrary input qubit into two optimal clones and one optimal flipped qubit. By combining linear and non-linear optical methods we experimentally implement a scheme that, after the cloning transformation, restores the original input qubit in one of the output channels, by using local measurements, classical communication and feedforward. This significant teleportation-like method demonstrates how the information is preserved during the cloning process. The realization of the reversion process is expected to find useful applications in the field of modern multi-partite quantum cryptography.Comment: 10 pages, 3 figure

Quantum Control of a Single Qubit

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a non-projective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realises the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.Comment: 12 pages, 7 figures, v2 includes new references and minor change

Single-bit Feedback and Quantum Dynamical Decoupling

Synthesizing an effective identity evolution in a target system subjected to unwanted unitary or non-unitary dynamics is a fundamental task for both quantum control and quantum information processing applications. Here, we investigate how single-bit, discrete-time feedback capabilities may be exploited to enact or to enhance quantum procedures for effectively suppressing unwanted dynamics in a finite-dimensional open quantum system. An explicit characterization of the joint unitary propagators correctable by a single-bit feedback strategy for arbitrary evolution time is obtained. For a two-dimensional target system, we show how by appropriately combining quantum feedback with dynamical decoupling methods, concatenated feedback-decoupling schemes may be built, which can operate under relaxed control assumptions and can outperform purely closed-loop and open-loop protocols.Comment: 12 pages, 2 figure

Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem

The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated. We provide a detailed analysis of their structure together with computable criteria for the separation of the two sets. When applied to O(d)-covariant channels this leads to a complete characterization and reveals a remarkable feature: instances of channels which are not in the convex hull of unitaries can return to it when either taking finitely many copies of them or supplementing with a completely depolarizing channel. In these scenarios this implies that a channel whose noise initially resists any environment-assisted attempt of correction can become perfectly correctable.Comment: 31 page

Optimality of private quantum channels

We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel $\cal E$ and von Neumann entropy of the ciphertext state $\varrho^{(0)}$. Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if exists) is optimizing the entropy. For non-ancillary single qubit PQC we have derived the optimal entropy for arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analyzed all the possible single qubit private quantum channels for arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.Comment: no commen

Reversibility of continuous-variable quantum cloning

We analyze a reversibility of optimal Gaussian $1\to 2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anti-clone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial LOCC reversal of the cloning and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $1\to M$ Gaussian cloning of coherent states which transforms it to optimal $1\to M'$ cloning for $M'<M$. Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.Comment: 7 pages, 5 figure

Formation of a two-dimensional oxide via oxidation of a layered material

We investigate the oxidation mechanism of the layered model system GeAs. In situ X-ray photoelectron spectroscopy experiments performed by irradiating an individual flake with synchrotron radiation in the presence of oxygen show that while As leaves the GeAs surface upon oxidation, a Ge-rich ultrathin oxide film is being formed in the topmost layer of the flake. We develop a theoretical model that supports the layer-by-layer oxidation of GeAs, with a logarithmic kinetics. Finally, assuming that the activation energy for the oxidation process changes linearly with coverage, we estimate that the activation energy for As oxidation is almost twice that for Ge at room temperature

Chemical exfoliation of MoS2 leads to semiconducting 1T' phase and not the metallic 1T phase

A trigonal phase existing only as small patches on chemically exfoliated few layer, thermodynamically stable 1H phase of MoS2 is believed to influence critically properties of MoS2 based devices. This phase has been most often attributed to the metallic 1T phase. We investigate the electronic structure of chemically exfoliated MoS2 few layered systems using spatially resolved (lesser than 120 nm resolution) photoemission spectroscopy and Raman spectroscopy in conjunction with state-of-the-art electronic structure calculations. On the basis of these results, we establish that the ground state of this phase is a small gap (~90 meV) semiconductor in contrast to most claims in the literature; we also identify the specific trigonal (1T') structure it has among many suggested ones