J. Ignacio Cirac

Experimental demonstration of quantum memory for light

The information carrier of todays communications, a weak pulse of light, is an intrinsically quantum object. As a consequence, complete information about the pulse cannot be perfectly recorded in a classical memory, even in principle. In the field of quantum information, this has led to the long-standing challenge of how to achieve a high-fidelity transfer of an independently prepared quantum state of light onto an atomic quantum state. Here we propose and experimentally demonstrate a protocol for such a quantum memory based on atomic ensembles. Recording of an externally provided quantum state of light onto the atomic quantum memory is achieved with 70 per cent fidelity, significantly higher than the limit for classical recording. Quantum storage of light is achieved in three steps: first, interaction of the input pulse and an entangling field with spin-polarized caesium atoms; second, subsequent measurement of the transmitted light; and third, feedback onto the atoms using a radio-frequency magnetic pulse conditioned on the measurement result. The density of recorded states is 33 per cent higher than the best classical recording of light onto atoms, with a quantum memory lifetime of up to 4 milliseconds.

Quantum computation and quantum-state engineering driven by dissipation

In quantum information science, dissipation is commonly viewed as an adverse effect that destroys information through decoherence. But theoretical work shows that dissipation can be used to drive quantum systems to a desired state, and therefore might serve as a resource in quantum computations. The strongest adversary in quantum information science is decoherence, which arises owing to the coupling of a system with its environment1. The induced dissipation tends to destroy and wash out the interesting quantum effects that give rise to the power of quantum computation2, cryptography2 and simulation3. Whereas such a statement is true for many forms of dissipation, we show here that dissipation can also have exactly the opposite effect: it can be a fully fledged resource for universal quantum computation without any coherent dynamics needed to complement it. The coupling to the environment drives the system to a steady state where the outcome of the computation is encoded. In a similar vein, we show that dissipation can be used to engineer a large variety of strongly correlated states in steady state, including all stabilizer codes, matrix product states4, and their generalization to higher dimensions5.

Density matrix renormalization group and periodic boundary conditions: a quantum information perspective.

We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which the results are dramatically improved. The picture also explains some features of the method in terms of entanglement and teleportation.

Area Laws in Quantum Systems: Mutual Information and Correlations

The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. In this Letter we show that this phenomenon not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of degrees of freedom, it may diverge as the inverse temperature in quantum systems. It is shown that an area law is generally implied by a finite correlation length when measured in terms of the mutual information.

Characterization of Gaussian operations and distillation of Gaussian states

We characterize the class of all physical operations that transform Gaussian states to Gaussian states. We show that this class coincides with that of all operations that can be performed on Gaussian states using linear optical elements and homodyne measurements. For bipartite systems we characterize the processes that can be implemented by local operations and classical communication, as well as those that can be implemented using positive partial transpose preserving maps. As an application, we show that Gaussian states cannot be distilled by local Gaussian operations and classical communication. We also define and characterize positive (but not completely positive) Gaussian maps.

Entanglement generated by dissipation and steady state entanglement of two macroscopic objects.

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.

Toward quantum superposition of living organisms

The most striking feature of quantum mechanics is the existence of superposition states, where an object appears to be in different situations at the same time. The existence of such states has been previously tested with small objects, such as atoms, ions, electrons and photons (Zoller et al 2005 Eur. Phys. J. D 36 203-28), and even with molecules (Arndt et al 1999 Nature 401 680-2). More recently, it has been shown that it is possible to create superpositions of collections of photons (Deleglise et al 2008 Nature 455 510-14), atoms (Hammerer et al 2008 arXiv:0807.3358) or Cooper pairs (Friedman et al 2000 Nature 406 43-6). Very recent progress in optomechanical systems may soon allow us to create superpositions of even larger objects, such as micro-sized mirrors or cantilevers (Marshall et al 2003 Phys. Rev. Lett. 91 130401; Kippenberg and Vahala 2008 Science 321 1172-6; Marquardt and Girvin 2009 Physics 2 40; Favero and Karrai 2009 Nature Photon. 3 201-5), and thus to test quantum mechanical phenomena at larger scales. Here we propose a method to cool down and create quantum superpositions of the motion of sub- wavelength, arbitrarily shaped dielectric objects trapped inside a high-finesse cavity at a very low pressure. Our method is ideally suited for the smallest living organisms, such as viruses, which survive under low-vacuum pressures (Rothschild and Mancinelli 2001 Nature 406 1092-101) and optically behave as dielectric objects (Ashkin and Dziedzic 1987 Science 235 1517-20). This opens up the possibility of testing the quantum nature of living organisms by

Classifying quantum phases using matrix product states and projected entangled pair states

We give a classification of gapped quantum phases of one-dimensional systems in the framework of Matrix Product States (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states, and both in the absence and presence of symmetries. We find that without symmetries, all systems are in the same phase, up to accidental ground state degeneracies. If symmetries are imposed, phases without symmetry breaking (i.e., with unique ground states) are classified by the cohomology classes of the symmetry group, this is, the equivalence classes of its projective representations, a result first derived in [X. Chen, Z.-C. Gu, and X.-G. Wen, Phys. Rev. B 83, 035107 (2011); arXiv:1008.3745]. For phases with symmetry breaking (i.e., degenerate ground states), we find that the symmetry consists of two parts, one of which acts by permuting the ground states, while the other acts on individual ground states, and phases are labelled by both the permutation action of the former and the cohomology class of the latter. Using Projected Entangled Pair States (PEPS), we subsequently extend our framework to the classification of twodimensional phases in the neighborhood of a number of important cases, in particular systems with unique ground states, degenerate ground states with a local order parameter, and topological order. We also show that in two dimensions, imposing symmetries does not constrain the phase diagram in the same way it does in one dimension. As a central tool, we introduce the isometric form, a normal form for MPS and PEPS which is a renormalization fixed point. Transforming a state to its isometric form does not change the phase, and thus, we can focus on to the classification of isometric forms.

Quantum correlations in two-fermion systems

We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank): i.e., we decompose the state into a combination of elementary Slater determinants formed by pairs of mutually orthogonal single-particle states. Mixed states can be characterized by their Slater number which is the minimal Slater rank required to generate them. For K = 2 we gi ve a necessary and sufficient condition for a state to have a Slater number 1. We introduce a correlation measure for mixed states which can be evaluated analytically for K = 2. For higher K, we provide a method of constructing and optimizing Slater number witnesses, i.e., operators that detect Slater numbers for some states.

Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects

We propose a method to prepare and verify spatial quantum superpositions of a nanometer-sized object separated by distances of the order of its size. This method provides unprecedented bounds for objective collapse models of the wave function by merging techniques and insights from cavity quantum optomechanics and matter-wave interferometry. An analysis and simulation of the experiment is performed taking into account standard sources of decoherence. We provide an operational parameter regime using present-day and planned technology.