Entanglement is the resource to overcome the restriction of operations to Local Operations assisted by Classical Communication (LOCC). The Maximally Entangled Set (MES) of states is the minimal set of n-partite pure states with the property that any truly n-partite entangled pure state can be obtained deterministically via LOCC from some state in this set. Hence, this set contains the most useful states for applications. In this work we characterize the MES for generic three qutrit states. Moreover, we analyze which generic three qutrit states are reachable (and convertible) under LOCC transformations. To this end we study reachability via separable operations (SEP), a class of operations that is strictly larger than LOCC. Interestingly, we identify a family of pure states that can be obtained deterministically via SEP but not via LOCC. To our knowledge these are the first examples of transformations among pure states that can be implemented via SEP but not via LOCC.

Spontaneous emission of a two-level atom in free space is modified by other atoms in its vicinity leading to super-and subradiance. In particular, for atomic distances closer than the transition wavelength the maximally entangled antisymmetric superposition state of two individually excited atomic dipole moments possesses no total dipole moment and will not decay spontaneously at all. Such a two-atom dark state does not exist, if the atoms feature additional decay channels towards other lower energy states. However, we show here that for any atomic state with N − 1 independent spontaneous decay channels one can always find a N -particle highly entangled state, which completely decouples from the free radiation field and does not decay. Moreover, we show that this state is the unique state orthogonal to the subspace spanned by the lower energy states with this property. Its subradiant behavior largely survives also at finite atomic distances. The decay of an excited atomic state towards lower lying states via spontaneous emission is one of the most striking consequences of the quantum nature of the free radiation field [1]. Heuristically introduced even before e.g. by Einstein, the spontaneous emission rate Γ = Interestingly, it turns out that for several particles the emission process is not independent but can be collectively enhanced or reduced depending on the atomic arrangement [3]. It was already noted some time ago that these superradiant and subradiant collective states, where a single excitation is distributed over many particles, are entangled atomic states [4,5]. Although a recent classical coupled dipole model also leads to subradiancelike phenomena [6], the most superradiant and the perfect dark states for two two-level atoms with states (|g , |e ) are the maximally entangled symmetric and antisymmetric dipole moment superposition statesWhile superradiance on a chosen transition persists in the case, when the atom possesses more than one decay channel, there is no completely dark state for two multilevel atoms with several decay channels from a single excited state |e to several lower lying states |g i as schematically depicted in Fig. 1. Hence, in practise the observation of subradiant states is much more difficult than seeing superradiance, as all other decay channels need to be excluded [7].In this paper, we introduce a new class of subradiant or dark states appearing for atoms with several independent transitions. As a key result of this work we find that for systems of N particles one can construct highly * Laurin.Ostermann@uibk.ac.at multi-partite entangled states, where all N − 1 independent decay channels are suppressed. For these states the total dipole moments on all of these N − 1 transitions simultaneously vanish and at least in principle the optical excitation in this state will be stored indefinitely.After introducing our model atom system and the generalized, unique multi-atom dark states, we will discuss their special entanglement properties and possible quantum information processing...

Magic states were introduced in the context of Clifford circuits as a resource that elevates classically simulatable computations to quantum universal capability, while maintaining the same gate set. Here we study magic states in the context of matchgate (MG) circuits, where the notion becomes more subtle, as MGs are subject to locality constraints and also the SWAP gate is not available. Nevertheless a similar picture of gate-gadget constructions applies, and we show that every pure fermionic state which is non-Gaussian, i.e. which cannot be generated by MGs from a computational basis state, is a magic state for MG computations. This result has significance for prospective quantum computing implementation in view of the fact that MG circuit evolutions coincide with the quantum physical evolution of non-interacting fermions. arXiv:1905.08584v1 [quant-ph]

Dipolar bilayers with antiparallel polarization, i.e. opposite polarization in the two layers, exhibit liquid-like rather than gas-like behavior. In particular, even without external pressure a self-bound liquid puddle of constant density will form. We investigate the symmetric case of two identical layers, corresponding to a two-component Bose system with equal partial densities. The zerotemperature equation of state E(ρ)/N , where ρ is the total density, has a minimum, with an equilibrium density that decreases with increasing distance between the layers. The attraction necessary for a self-bound liquid comes from the inter-layer dipole-dipole interaction that leads to a mediated intra-layer attraction. We investigate the regime of negative pressure towards the spinodal instability, where the bilayer is unstable against infinitesimal fluctuations of the total density, conformed by calculations of the speed of sound of total density fluctuations.

The notion of compressed quantum computation is employed to simulate the Ising interaction of a 1D-chain consisting out of n qubits using the universal IBM cloud quantum computer running on log(n) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer. As a solution, we propose to use validating circuits, that is to run independent controlled quantum circuits of similar complexity to the circuit of interest.The faithful simulation of quantum systems remains one of the most interesting problems that can be addressed with a full-fledged quantum computer. Phenomena such as superconductivity in two dimensions, highly frustrated condensed matter systems or the effect of topology in quantum systems are out of the reach of classical simulation. The emergence of new designs for quantum computation further motivates more detailed studies of mapping quantum problems to realistic quantum computation.A particular instance of relevant physics that can be addressed with a quantum computation is the study of quantum phase transitions [1]. Indeed, some systems undergo a quantum phase transition which is characterized by large quantum correlations at zero temperature. At their critical point, conformal symmetry is restored and correlations decay algebraically and become long-ranged. Furthermore, the entanglement entropy of the ground state of the system diverges in the thermodynamic limit at the phase transition. In general, such a large amount of entanglement cannot be described correctly in two dimensions by classical means.Several experimental set-ups are currently employed to investigate quantum phase transitions [2][3][4]. This poses the problem of designing refined experiments, which have so far tended to exploit the avenue of quantum simulation, rather than quantum computation. One of the reasons for that is that universal quantum computation, which can be used to simulate any system, is currently restricted to approximately ten qubits [5]. However, as we will also exploit here, certain simulations can be compressed and run on an exponentially smaller universal quantum computer.A particularly interesting new approach to the use of quantum computers is the advent of cloud quantum computation. The free access to run quantum circuits on a remote cloud computer opens the door to design new algorithms, to improve them by trial and error, and to refute or consolidate non-obvious ideas. It may be argued that cloud quantum computation plays a similar role to the introduction of personal computers or open mainframes in the early stages of informatics.At present, the availability of cloud quantum comput...

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The characterization of transformations among entangled pure states via local operations assisted by classical communication (LOCC) is a crucial problem in quantum information theory for both theoretical and practical reasons. As LOCC has a highly intricate structure, sometimes the larger set of separable (SEP) maps is considered, which has a mathematically much simpler description. In the literature, mainly SEP maps consisting of invertible Kraus operators have been taken into account. In this paper we show that the consideration of those maps is not sufficient when deciding whether a state can be mapped to another via general SEP transformations. This is done by providing explicit examples of transformations among pure three- and five-qubit states, which are feasible via SEP maps containing singular Kraus operators, however, not possible via SEP maps containing solely regular Kraus operators. The key point that allows to construct the SEP maps is to introduce projective measurements that occur with probability zero on the input state. The fact that it is not sufficient to consider SEP maps composed out of regular Kraus operators even in the case of pure state transformations, also affects the results on LOCC transformations among pure states. However, we show that non-invertible Kraus operators do not help in state transformations under LOCC with finitely many rounds of classical communication, i.e. the necessary and sufficient condition for SEP transformations with invertible Kraus operators is still a necessary condition for convertibility under finite-round LOCC. Moreover, we show that the results on transformations via SEP that are not possible with LOCC (including infinitely many rounds of classical communication) presented in Hebenstreit et al 2016 Phys. Rev. A 93, 012339 are not affected.

Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a non-vanishing probability. The classes obtained in this way are called SLOCC classes. They can be categorized into three disjoint types: the null-cone, the polystable states and strictly semistable states. Whereas the former two are well characterized, not much is known about strictly semistable states. We derive a criterion for the existence of the latter. In particular, we show that there exists a strictly semistable state if and only if there exist two polystable states whose orbits have different dimensions. We illustrate the usefulness of this criterion by applying it to tripartite states where one of the systems is a qubit. Moreover, we scrutinize all SLOCC classes of these systems and derive a complete characterization of the corresponding orbit types. We present representatives of strictly semistable classes and show to which polystable state they converge via local regular operators.