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Marie Ericsson

Publications and source records attributed to Marie Ericsson.

At least 19 recordsLinked to original sources
arXiv2018

Environmental design principles for efficient excitation energy transfer in dimer and trimer pigment-protein molecular aggregates and the relation to non-Markovianity

In this study, we explore optimal environments for efficient EET between end sites in a number of dimer and trimer model pigment-protein molecular aggregates when the EET dynamics is modeled by the HEOM-method. For these optimal environmental parameters, we further quantify the non-Markovianity by the BLP-measure to elucidate its possible connection to efficient EET. We also quantify coherence in the pigment systems by means of the measure l1-norm of coherence to analyze its interplay with environmental effects when EET efficiency is maximal. Our aim is to investigate possible environmental design principles for achieving efficient EET in model pigment-protein molecular aggregates and to determine whether non-Markovianity is a possible underlying resource in such systems. We find that the structure of the system Hamiltonian (i.e., the pigment Hamiltonian parameter space) and especially, the relationship between the site excitation energies, determines whether one of two specific environmental regimes is the most beneficial in promoting efficient EET in these model systems. In the first regime, optimal environmental conditions are such that the EET dynamics in the system is left as coherent as possible. In the second regime, the most advantageous role of the environment is to drive the system towards equilibrium as fast as possible. In reality, optimal environmental conditions may involve a combination of these two effects. We cannot establish a relation between efficient EET and non-Markovianity, i.e., non-Markovianity cannot be regarded as a resource in the systems investigated in this study.

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arXiv2016

Geometric Phases for Mixed States of the Kitaev Chain

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyze the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyze the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

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arXiv2014

Classification scheme of pure multipartite states based on topological phases

We investigate the connection between the concept of affine balancedness (a-balancedness) introduced in [Phys. Rev A. {\bf 85}, 032112 (2012)] and polynomial local SU invariants and the appearance of topological phases respectively. It is found that different types of a-balancedness correspond to different types of local SU invariants analogously to how different types of balancedness as defined in [New J. Phys. {\bf 12}, 075025 (2010)] correspond to different types of local SL invariants. These different types of SU invariants distinguish between states exhibiting different topological phases. In the case of three qubits the different kinds of topological phases are fully distinguished by the three-tangle together with one more invariant. Using this we present a qualitative classification scheme based on balancedness of a state. While balancedness and local SL invariants of bidegree $(2n,0)$ classify the SL-semistable states [New J. Phys. {\bf 12}, 075025 (2010), Phys. Rev. A {\bf 83} 052330 (2011)], a-balancedness and local SU invariants of bidegree $(2n-m,m)$ gives a more fine grained classification. In this scheme the a-balanced states form a bridge from the genuine entanglement of balanced states, invariant under the SL-group, towards the entanglement of unbalanced states characterized by U invariants of bidegree $(n,n)$. As a by-product we obtain generalizations to the W-state, states that are entangled, but contain only globally distributed entanglement of parts of the system.

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arXiv2013

Comment on `Detecting non-Abelian geometric phases with three-level $Λ$ systems'

In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)] claim to have found a non-Abelian adiabatic geometric phase associated with the energy eigenstates of a large-detuned $Λ$ three-level system. They further propose a test to detect the non-commutative feature of this geometric phase. On the contrary, we show that the non-Abelian geometric phase picked up by the energy eigenstates of a $Λ$ system is trivial in the adiabatic approximation, while, in the exact treatment of the time evolution, this phase is very small and cannot be separated from the non-Abelian dynamical phase acquired along the path in parameter space.

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arXiv2013

Robustness of non-adiabatic holonomic gates

The robustness to different sources of error of the scheme for non-adiabatic holonomic gates proposed in [New J. Phys. {\bf 14}, 103035 (2012)] is investigated. Open system effects as well as errors in the driving fields are considered. It is found that the gates can be made error resilient by using sufficiently short pulses. The principal limit of how short the pulses can be made is given by the breakdown of the quasi-monochromatic approximation. A comparison with the resilience of adiabatic gates is carried out.

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arXiv2012

Topological phases and multiqubit entanglement

Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multi-qubit systems as the result of cyclic local $\rm{SU(2)}$ evolution. These phases originate from the topological structure of the local $\rm{SU(2)}$-orbits and are an attribute of most entangled multi-qubit systems. We discuss the relation between topological phases and SLOCC-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an $n$-qubit system is described and a complete list of these phases for up to seven qubits is given.

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arXiv2011

Global asymmetry of many-qubit correlations: A lattice gauge theory approach

We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.

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arXiv2011

Open system effects on slow light and electromagnetically induced transparency

The coherence properties of a three-level $Λ$-system influenced by a Markovian environment are analyzed. A coherence vector formalism is used and a vector form of the Lindblad equation is derived. Together with decay channels from the upper state, open system channels acting on the subspace of the two lower states are investigated, i.e., depolarization, dephasing, and amplitude damping channels. We derive an analytic expression for the coherence vector and the concomitant optical susceptibility, and analyze how the different channels influence the optical response. This response depends non-trivially on the type of open system interaction present, and even gain can be obtained. We also present a geometrical visualization of the coherence vector as an aid to understand the system response.

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arXiv2011

Geometric local invariants and pure three-qubit states

We explore a geometric approach to generating local SU(2) and $SL(2,\mathbb{C})$ invariants for a collection of qubits inspired by lattice gauge theory. Each local invariant or 'gauge' invariant is associated to a distinct closed path (or plaquette) joining some or all of the qubits. In lattice gauge theory, the lattice points are the discrete space-time points, the transformations between the points of the lattice are defined by parallel transporters and the gauge invariant observable associated to a particular closed path is given by the Wilson loop. In our approach the points of the lattice are qubits, the link-transformations between the qubits are defined by the correlations between them and the gauge invariant observable, the local invariants associated to a particular closed path are also given by a Wilson loop-like construction. The link transformations share many of the properties of parallel transporters although they are not undone when one retraces one's steps through the lattice. This feature is used to generate many of the invariants. We consider a pure three qubit state as a test case and find we can generate a complete set of algebraically independent local invariants in this way, however the framework given here is applicable to mixed states composed of any number of $d$ level quantum systems. We give an operational interpretation of these invariants in terms of observables.

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arXiv2011

Correlation induced non-Abelian quantum holonomies

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase [2004 {\it J. Phys. A: Math. Gen.} {\bf 37} 1821] in the case of two-qubit systems undergoing local SU(2) evolutions.

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arXiv2007

Continuous variable entanglement sharing in non-inertial frames

We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that for two observers undergoing finite acceleration, the entanglement vanishes between the lowest frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and unaccessible modes from a non-inertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.

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arXiv2007

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e. simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N >= 4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding and potential exploitation of shared quantum correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states), exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.

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arXiv2007

Optical implementation and entanglement distribution in Gaussian valence bond states

We study Gaussian valence bond states of continuous variable systems, obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of $N$ sites of an harmonic chain. The entanglement distribution in Gaussian valence bond states can be controlled by varying the input amount of entanglement engineered in a (2M+1)-mode Gaussian state known as the building block, which is isomorphic to the projector applied at a given site. We show how this mechanism can be interpreted in terms of multiple entanglement swapping from the chain of ancillary bonds, through the building blocks. We provide optical schemes to produce bisymmetric three-mode Gaussian building blocks (which correspond to a single bond, M=1), and study the entanglement structure in the output Gaussian valence bond states. The usefulness of such states for quantum communication protocols with continuous variables, like telecloning and teleportation networks, is finally discussed.

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arXiv2006

Entanglement in Gaussian matrix-product states

Gaussian matrix product states are obtained as the outputs of projection operations from an ancillary space of M infinitely entangled bonds connecting neighboring sites, applied at each of N sites of an harmonic chain. Replacing the projections by associated Gaussian states, the 'building blocks', we show that the entanglement range in translationally-invariant Gaussian matrix product states depends on how entangled the building blocks are. In particular, infinite entanglement in the building blocks produces fully symmetric Gaussian states with maximum entanglement range. From their peculiar properties of entanglement sharing, a basic difference with spin chains is revealed: Gaussian matrix product states can possess unlimited, long-range entanglement even with minimum number of ancillary bonds (M=1). Finally we discuss how these states can be experimentally engineered from N copies of a three-mode building block and N two-mode finitely squeezed states.

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arXiv2005

Local Cloning of Arbitrarily Entangled Multipartite States

We examine the perfect cloning of non-local, orthogonal states with only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to distinguishability. We also consider the case of catalytic cloning, which we show provides no enhancement to the set of clonable states.

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arXiv2005

Geometric Effects and Computation in Spin Networks

When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by performing rotations on the spin. Such effects can be used to determine properties of the chain, such as its length, in a robust manner. Alternatively, they can form the basis of a spin network quantum computer. We demonstrate a universal set of gates in such a system by both dynamical and geometrical means.

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arXiv2004

Measurement of geometric phase for mixed states using single photon interferometry

Geometric phase may enable inherently fault-tolerant quantum computation. However, due to potential decoherence effects, it is important to understand how such phases arise for {\it mixed} input states. We report the first experiment to measure mixed-state geometric phases in optics, using a Mach-Zehnder interferometer, and polarization mixed states that are produced in two different ways: decohering pure states with birefringent elements; and producing a nonmaximally entangled state of two photons and tracing over one of them, a form of remote state preparation.

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