arXiv subjects

Peter D. Johnson

Publications and source records attributed to Peter D. Johnson.

42 records · Page 3Linked to original sources

arXiv2016

Alternating Projections Methods for Discrete-time Stabilization of Quantum States

We study sequences (both cyclic and randomized) of idempotent completely-positive trace-preserving quantum maps, and show how they asymptotically converge to the intersection of their fixed point sets via alternating projection methods. We characterize the robustness features of the protocol against randomization and provide basic bounds on its convergence speed. The general results are then specialized to stabilizing en- tangled states in finite-dimensional multipartite quantum systems subject to a resource constraint, a problem of key interest for quantum information applications. We conclude by suggesting further developments, including techniques to enlarge the set of stabilizable states and ensure efficient, finite-time preparation.

quant-ph↗

arXiv2016

General fixed points of quasi-local frustration-free quantum semigroups: from invariance to stabilization

We investigate under which conditions a mixed state on a finite-dimensional multipartite quantum system may be the unique, globally stable fixed point of frustration-free semigroup dynamics subject to specified quasi-locality constraints. Our central result is a linear-algebraic necessary and sufficient condition for a generic (full-rank) target state to be frustration-free quasi-locally stabilizable, along with an explicit procedure for constructing Markovian dynamics that achieve stabilization. If the target state is not full-rank, we establish sufficiency under an additional condition, which is naturally motivated by consistency with pure-state stabilization results yet provably not necessary in general. Several applications are discussed, of relevance to both dissipative quantum engineering and information processing, and non-equilibrium quantum statistical mechanics. In particular, we show that a large class of graph product states (including arbitrary thermal graph states) as well as Gibbs states of commuting Hamiltonians are frustration-free stabilizable relative to natural quasi-locality constraints. Likewise, we provide explicit examples of non-commuting Gibbs states and non-trivially entangled mixed states that are stabilizable despite the lack of an underlying commuting structure, albeit scalability to arbitrary system size remains in this case an open question.

quant-ph↗

arXiv2014

Atom-Wide Co Wires on Cu(775) at Room Temperature

We report on a new surface phase of the Co-vicinal-Cu(111) system which exhibits self-assembled uniform Co quantum wires that are stable at 300K. STM-imaging measurements show that wires will self-assemble within a narrow range of Co coverage and, within this range, the wires increase in length as coverage is increased. The STM images show that the wires form along the leading edge of the step rise, differentiating it from previously theoretically predicted atomic-wire phases. The formation of relatively long laterally un-encapsulated one- and two-atom wires also differentiates it from past experimentally observed step-island formation. Furthermore, our experiments also show directly that the Co wires coexist with another Co phase that had been previously predicted for growth on Cu(111). Our observations allow us to comment on the formation kinetics of the atomic-wire phase and on the fit of our data to a recently developed lattice-gas model.

cond-mat.mtrl-sci↗

arXiv2014

The Nature of Surface States on Vicinal Cu (775): An STM and Photoemission Study

We report ARPES and a set of in situ STM measurements on a narrow-terrace-width vicinal Cu(111) crystal surface, Cu(775), whose vicinal cut lies close to the transition between terrace and step modulation. These measurements show sharp zone-folding (or Umklapp) features with a periodicity in k||, indicating that the predominant reference plane is that of Cu(775), i.e. that the surface is predominately step-modulated. Our measurements also show variation in Umklapp intensity with photon energy, which is consistent with prior ARPES experiments on other vicinal Cu(111) surfaces and in agreement with our designation of the state as being step modulated. The measurements also show a weak terrace-modulated state, which, based on several characteristics, we attribute to the presence of terrace widths larger than the ideal terrace width. By measuring the intensity ratio of the two distinct surface-state modulations from PE and the terrace-width distribution from STM, we derive a value for the terrace width, at which the surface-state switches between the two modulations.

cond-mat.mes-hall↗

arXiv2013

Compatible quantum correlations: on extension problems for Werner and isotropic states

We investigate some basic scenarios in which a given set of bipartite quantum states may consistently arise as the set of reduced states of a global N-partite quantum state. Intuitively, we say that the multipartite state "joins" the underlying correlations. Determining whether, for a given set of states and a given joining structure, a compatible N-partite quantum state exists is known as the quantum marginal problem. We restrict to bipartite reduced states that belong to the paradigmatic classes of Werner and isotropic states in d dimensions, and focus on two specific versions of the quantum marginal problem which we find to be tractable. The first is Alice-Bob, Alice-Charlie joining, with both pairs being in a Werner or isotropic state. The second is m-n sharability of a Werner state across N subsystems, which may be seen as a variant of the N-representability problem to the case where subsystems are partitioned into two groupings of m and n parties, respectively. By exploiting the symmetry properties that each class of states enjoys, we determine necessary and sufficient conditions for three-party joinability and 1-n sharability for arbitrary d. Our results explicitly show that although entanglement is required for sharing limitations to emerge, correlations beyond entanglement generally suffice to restrict joinability, and not all unentangled states necessarily obey the same limitations. The relationship between joinability and quantum cloning as well as implications for the joinability of arbitrary bipartite states are discussed.

quant-ph↗

arXiv2012

Spin-exchange-induced dimerization of an atomic 1-D system

Using low-temperature scanning tunneling microscopy, we demonstrate an unambiguous 1-D system that surprisingly undergoes a CDW instability on a metallic substrate. Our ability to directly and quantitatively measure the structural distortion of this system provides an accurate reference for comparison with first principles theory. In comparison to previously proposed physical mechanisms, we attribute this particular 1-D CDW instability to a ferromagnetic state. We show that though the linear arrayed dimers are not electronically isolated, they are magnetically independent, and hence can potentially serve as a binary spin-memory system.

cond-mat.str-el↗