Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAsymptotic Evolution of Random Unitary Operations
140
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
rate research
Read More
We review the generation of random pure states using a protocol of repeated two qubit gates. We study the dependence of the convergence to states with Haar multipartite entanglement distribution. We investigate the optimal generation of such states in terms of the physical (real) time needed to apply the protocol, instead of the gate complexity point of view used in other works. This physical time can be obtained, for a given Hamiltonian, within the theoretical framework offered by the quantum brachistochrone formalism. Using an anisotropic Heisenberg Hamiltonian as an example, we find that different optimal quantum gates arise according to the optimality point of view used in each case. We also study how the convergence to random entangled states depends on different entanglement measures.
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any unitary operator, which commutes with translations, and couples only sites at a finite distance from each other. For example, a single step of the walk could be composed of any finite succession of different shift and coin operations in the usual sense, with any lattice dimension and coin dimension. We find ballistic scaling, and establish a direct method for computing the asymptotic distribution of position divided by time, namely as the distribution of the discrete time analog of the group velocity. In the random case, we let a Markov chain (control process) pick in each step one of finitely many unitary walks, in the sense described above. In ballistic order we find a non-random drift, which depends only on the mean of the control process and not on the initial state. In diffusive scaling the limiting distribution is asymptotically Gaussian, with a covariance matrix (diffusion matrix) depending on momentum. The diffusion matrix depends not only on the mean but also on the transition rates of the control process. In the non-random limit, i.e., when the coins chosen are all very close, or the transition rates of the control process are small, leading to long intervals of ballistic evolution, the diffusion matrix diverges. Our method is based on spatial Fourier transforms, and the first and second order perturbation theory of the eigenvalue 1 of the transition operator for each value of the momentum.
The realism-based nonlocality (RBN) is a recently introduced measure that differs from the well-known Bells nonlocality. For bipartite states, the RBN concerns how much an element of reality associated with a given observable is affected upon local measurements on a subsystem. Here, we present an analytical proof for the unitary invariance of the RBN and that it presents a monotonous behavior upon the action of unital and non-unital local quantum noise. We illustrate our results by employing the two-qubits Werner state and thermal quantum correlated states. We show how the RBN is limited by the initial equilibrium temperature and, especially, that it decays asymptotically with it. These results also corroborate the hierarchy relationship between the quantifiers of RBN and global quantum discord, showing that RBN can capture undetectable nonlocal aspects even for non-discordant states. Finally, we argue how our results can be employed to use the RBN as a security tool in quantum communication tasks.
We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimensional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations.
We study the power of dephasing-covariant operations in the resource theories of coherence and entanglement. These are quantum operations whose actions commute with a projective measurement. In the resource theory of coherence, we find that any two states are asymptotically interconvertible under dephasing-covariant operations. This provides a rare example of a resource theory in which asymptotic reversibility can be attained without needing the maximal set of resource non-generating operations. When extended to the resource theory of entanglement, the resultant operations share similarities with LOCC, such as prohibiting the increase of all Renyi $alpha$-entropies of entanglement under pure state transformations. However, we show these operations are still strong enough to enable asymptotic reversibility between any two maximally correlated mixed states, even in the multipartite setting.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
