We present a method of simulating the Dirac equation in 3+1 dimensions for a free spin-1/2 particle in a single trapped ion. The Dirac bispinor is represented by four ionic internal states, and position and momentum of the Dirac particle are associated with the respective ionic variables. We show also how to simulate the simplified 1+1 case, requiring the manipulation of only two internal levels and one motional degree of freedom. Moreover, we study relevant quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the transition from massless to massive fermions, and the relativistic and nonrelativistic limits, via the tuning of controllable experimental parameters.
A quantum simulator is a device engineered to reproduce the properties of an
ideal quantum model. It allows the study of quantum systems that cannot be
efficiently simulated on classical computers. While a universal quantum
computer is also a quantum simulator, only particular systems have been
simulated up to now. Still, there is a wealth of successful cases, such as spin
models, quantum chemistry, relativistic quantum physics and quantum phase
transitions. Here, we show how to design a quantum simulator for the Majorana
equation, a non-Hamiltonian relativistic wave equation that might describe
neutrinos and other exotic particles beyond the standard model. The simulation
demands the implementation of charge conjugation, an unphysical operation that
opens a new front in quantum simulations, including the discrete symmetries
associated with complex conjugation and time reversal. Finally, we show how to
implement this general method in trapped ions.Comment: To be published in Physical Review
A field in the vacuum state, which is in principle separable, can evolve to an entangled state in a dynamical gravitational collapse. We will study, quantify, and discuss the origin of this entanglement, showing that it could even reach the maximal entanglement limit for low frequencies or very small black holes, with consequences in micro-black hole formation and the final stages of evaporating black holes. This entanglement provides quantum information resources between the modes in the asymptotic future (thermal Hawking radiation) and those which fall to the event horizon. We will also show that fermions are more sensitive than bosons to this quantum entanglement generation. This fact could be helpful in finding experimental evidence of the genuine quantum Hawking effect in analog models.
We propose an inductive procedure to classify N −partite entanglement under stochastic local operations and classical communication (SLOCC) provided such a classification is known for N − 1 qubits. The method is based upon the analysis of the coefficient matrix of the state in an arbitrary product basis. We illustrate this approach in detail with the well-known bi-and tripartite systems, obtaining as a by-product a systematic criterion to establish the entanglement class of a given pure state without resourcing to any entanglement measure. The general case is proved by induction, allowing us to find an upper bound for the number of N -partite entanglement classes in terms of the number of entanglement classes for N − 1 qubits.
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