Borivoje Dakic

Experimental boson sampling

The boson-sampling problem is experimentally solved by implementing Aaronson and Arkhipovs model of computation with photons in integrated optical circuits. These results set a benchmark for a type of quantum computer that can potentially outperform a conventional computer by using only a few photons and linear optical elements.

Quantum discord as resource for remote state preparation

Quantum discord is the total non-classical correlation between two systems. This includes, but is not limited to, entanglement. Photonic experiments now demonstrate that separable states with non-zero quantum discord are a useful resource for quantum information processing and can even outperform entangled states.

Deep Beauty: Quantum Theory and Beyond: Is Entanglement Special?

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.

Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems

Quantum simulations, where one quantum system is used to emulate another, are starting to become experimentally feasible. Here, four-photon states are used to simulate spin tetramers, which are important in the description of certain solid-state systems. Emerging frustration within the tetramer is observed, as well as evolution of the ground state from a localized to a resonating-valence-bond state.

A two-qubit photonic quantum processor and its application to solving systems of linear equations

Stefanie Barz, Ivan Kassal, Martin Ringbauer1,∗, Yannick Ole Lipp, Borivoje Dakić, Alán Aspuru-Guzik, Philip Walther 1 Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria 2 Department of Chemistry and Chemical Biology, Harvard University, Cambridge MA 02138, United States 3 Centre for Engineered Quantum Systems, Centre for Quantum Computing and Communication Technology, and School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, Australia ∗ Present address: Centre for Engineered Quantum Systems, Centre for Quantum Computing and Communication Technology, and School of Mathematics and Physics, The University of Queensland, St Lucia QLD 4072, AustraliaLarge-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations.

Theories of systems with limited information content

We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary measurements, i.e. a complete knowledge of future outcome in one measurement is at the expense of complete uncertainty in the others. This is a characteristic feature of the theories and they can be ordered according to the number of mutually complementary measurements, which is also shown to define their computational abilities. In the theories multipartite states may contain entanglement, and tomography with local measurements is possible. The classification includes both classical and quantum theory and also generalized probabilistic theories with a higher number of degrees of freedom, for which operational meaning is given. We also discuss thought experiments discriminating standard quantum theory from the generalizations.

Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models

Mutually unbiased bases encapsulate the concept of complementarity - the impossibility of simultaneous knowledge of certain observables - in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.

Density cubes and higher-order interference theories

Can quantum theory be seen as a special case of a more general probabilistic theory, as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of interference they exhibit as proposed by Sorkin. A simple operational argument shows that the theories require higher-order tensors as a representation of physical states. For the third-order interference we derive an explicit theory of ‘density cubes’ and show that quantum theory, i.e. theory of density matrices, is naturally embedded in it. We derive the genuine non-quantum class of states and nontrivial dynamics for the case of a three-level system and show how one can construct the states of higher dimensions. Additionally to genuine third-order interference, the density cubes are shown to violate the Leggett–Garg inequality beyond the quantum Tsirelson bound for temporal correlations.

The Classical Limit of a Physical Theory and the Dimensionality of Space

In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the “elementary systems” and the physical space in which “laboratory devices” are embedded. Each of those spaces has its own dimension—the minimal number of real parameters (coordinates) needed to specify the state of system or a point within the physical space. Within an operational framework to a physical theory, the two dimensions coincide in a natural way under the following “closeness” requirement: the dynamics of a single elementary system can be generated by the invariant interaction between the system and the “macroscopic transformation device” that itself is described from within the theory in the macroscopic (classical) limit. Quantum mechanics fulfils this requirement since an arbitrary unitary transformation of an elementary system (spin-1/2 or qubit) can be generated by the pairwise invariant interaction between the spin and the constituents of a large coherent state (“classical magnetic field”). Both the spin state space and the “classical field” are then embedded in the Euclidean three-dimensional space. Can we have a general probabilistic theory, other than quantum theory, in which the elementary system (“generalized spin”) and the “classical fields” generating its dynamics are embedded in a higher-dimensional physical space? We show that as long as the interaction is pairwise, this is impossible, and quantum mechanics and the three-dimensional space remain the only solution. However, having multi-particle interactions and a generalized notion of “classical field” may open up such a possibility.

Efficient hidden-variable simulation of measurements in quantum experiments.

We prove that the results of a finite set of general quantum measurements on an arbitrary dimensional quantum system can be simulated using a polynomial (in measurements) number of hidden-variable states. In the limit of infinitely many measurements, our method gives models with the minimal number of hidden-variable states, which scales linearly with the number of measurements. These results can find applications in foundations of quantum theory, complexity studies, and classical simulations of quantum systems.