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Register a new userState Transfer in Highly Connected Networks and a Quantum Babinet Principle
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The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size N, whose structure is that of a N/2-cross polytope graph, if N is a multiple of 4. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.
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We study the routing of quantum information in parallel on multi-dimensional networks of tunable qubits and oscillators. These theoretical models are inspired by recent experiments in superconducting circuits using Josephson junctions and resonators. We show that perfect parallel state transfer is possible for certain networks of harmonic oscillator modes. We further extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is both optimal and robust in the presence of dissipation and finite bandwidth.
In quantum logic, introduced by Birkhoff and von Neumann, De Morgans Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeutis quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeutis quantum set theory has a problem in that De Morgans Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for bounded quantifiers that satisfies De Morgans Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgans Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgans Laws.
We investigate the quantum state transfer in a chain of particles satisfying q-deformed oscillators algebra. This general algebraic setting includes the spin chain and the bosonic chain as limiting cases. We study conditions for perfect state transfer depending on the number of sites and excitations on the chain. They are formulated by means of irreducible representations of a quantum algebra realized through Jordan-Schwinger maps. Playing with deformation parameters, we can study the effects of nonlinear perturbations or interpolate between the spin and bosonic chain.
Quantum state transfer between distant nodes is at the heart of quantum processing and quantum networking. Stimulated by this, we propose a scheme where one can highly achieve quantum state transfer between sites in a cavity quantum optomechanical network. There, each individual cell site is composed of a localized mechanical mode which interacts with a laser-driven cavity mode via radiation pressure, and photons exchange between neighboring sites is allowed. After the diagonalization of the Hamiltonian of each cell, we show that the system can be reduced to an effective Hamiltonian of two decoupled bosonic chains, and therefore we can apply the well-known results regarding quantum state transfer in conjuction with an additional condition on the transfer times. In fact, we show that our transfer protocol works for any arbitrary quantum state, a result that we will illustrate within the red sideband regime. Finally, in order to give a more realistic scenario we take into account the effects of independent thermal reservoirs for each site. Thus, solving the standard master equation within the Born-Markov approximation, we reassure both the effective model as well as the feasibility of our protocol.
We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially-separated nodes of a quantum network. The transmission protocol employs special laser pulses which excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wavepacket that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.
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