arXiv subjects

Vahid Karimipour

Publications and source records attributed to Vahid Karimipour.

At least 55 records · Page 3Linked to original sources

arXiv2015

Quantum phase transition in the $Z_3$ Kitaev-Potts model

The stability of the topological order phase induced by the $Z_3$ Kitaev model, which is a candidate for fault-tolerant quantum computation, against the local order phase induced by the 3-State Potts model is studied. We show that the low energy sector of the Kitaev-Potts model is mapped to the Potts model in the presence of transverse magnetic field. Our study relies on two high-order series expansion based on continuous unitary transformations in the limits of small- and large-Potts couplings as well as mean-field approximation. Our analysis reveals that the topological phase of the $Z_3$ Kitaev model breaks down to the Potts model through a first order phase transition. We capture the phase transition by analysis of the ground state energy, one-quasiparticle gap and geometric measure of entanglement.

quant-ph↗

arXiv2014

A comparison of parallel and anti-parallel two qubit mixed states

We investigate the correlation properties of separable two qubit states with maximally mixed marginals. These states are divided to two sets with the same geometric quantum correlation. However a closer scrutiny of these states reveals a profound difference between their quantum correlations as measured by more probing measures. Although these two sets of states are prepared by the same type of quantum operations acting on classically correlated states with equal classical correlations, the amount of final quantum correlation is different. We investigate this difference and trace it back to the hidden classical correlation which exists in their preparation process. We also compare these states with regard to their usefulness for entanglement distribution and their robustness against noise.

quant-ph↗

arXiv2013

The Kitaev-Ising model, Transition between topological and ferromagnetic order

We study the Kitaev-Ising model, where ferromagnetic Ising interactions are added to the Kitaev model on a lattice. This model has two phases which are characterized by topological and ferromagnetic order. Transitions between these two kinds of order are then studied on a quasi-one dimensional system, a ladder, and on a two dimensional periodic lattice, a torus. By exactly mapping the quasi-one dimensional case to an anisotropic XY chain we show that the transition occurs at zero $λ$ where $λ$ is the strength of the ferromagnetic coupling. In the two dimensional case the model is mapped to a 2D Ising model in transverse field, where it shows a transition at finite value of $λ$. A mean field treatment reveals the qualitative character of the transition and an approximate value for the transition point. Furthermore with perturbative calculation, we show that expectation value of Wilson loops behave as expected in the topological and ferromagnetic phases.

quant-ph↗

arXiv2012

The power of quantum channels for creating quantum correlations

Local noise can produce quantum correlations on an initially classically correlated state, provided that it is not represented by a unital or semi-classical channel \cite{DagmarBruss}. We find the power of any given local channel for producing quantum correlations on an initially classically correlated state. We introduce a computable measure for quantifying the quantum correlations in quantum-classical states, which is based on the non-commutativity of ensemble states in one party of the composite system. Using this measure we show that the amount of quantum correlations produced, is proportional to the classical correlations in the initial state. The power of an arbitrary channel for producing quantum correlations is found by averaging over all possible initial states. Finally we compare our measure with the geometrical measure of quantumness for a subclass of quantum-classical sates, for which we have been able to find a closed analytical expression.

quant-ph↗

arXiv2012

Noise effects in perfect transmission of quantum states

A recent scheme for perfect transmission of quantum states through quasi-one dimensional chains requires application of global control at regular intervals of time. We study the effect of stochastic noise in this control and find that the scheme is robust for reasonable values of disorder. Both un-correlated and correlated noise in the external control are studied and it is remarkably found that the efficiency of the protocol is much higher in presence of correlated noise.

quant-ph↗

arXiv2012

Completeness of classical $ϕ^4$ theory on 2D lattices

We formulate a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then show that the discrete version of $ϕ^4$ theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model. To achieve this, we extend the recently proposed quantum formalism for the Ising model \cite{quantum formalism} and its completeness property \cite{completeness} to the continuous variable case.

quant-ph↗

arXiv2011

Secure quantum carriers for quantum state sharing

We develop the concept of quantum carrier and show that messages can be uploaded and downloaded from this carrier and while in transit, these messages are hidden from external agents. We explain in detail the working of the quantum carrier for different communication tasks, including quantum key distribution, classical secret and quantum state sharing among a set of $n$ players according to general threshold schemes. The security of the protocol is discussed and it is shown that only the legitimate subsets can retrieve the secret messages, the collaboration of all the parties is needed for the continuous running of the protocol and maintaining the carrier.

quant-ph↗

arXiv2011

Linking Classical and Quantum Stochastic Processes

We define a map which relates four dimensional classical stochastic matrices to qubit quantum channels. The map preserves the spectrum and the composition of processes. To do this we introduce the concept of Bloch tetrahedron which plays the same role in the classical context as the Bloch sphere in the quantum context. A similar map is also induced between dynamical generators of classical and quantum stochastic processes. Possibilities for generalization to arbitrary dimensions are also discussed.

quant-ph↗

arXiv2011

Characterization of qutrit channels in terms of their covariance and symmetry properties

We characterize the completely positive trace-preserving maps on qutrits (qutrit channels) according to their covariance and symmetry properties. Both discrete and continuous groups are considered. It is shown how each symmetry group restricts arbitrariness in the parameters of the channel to a very small set. Although the explicit examples are related to qutrit channels, the formalism is sufficiently general to be applied to qudit channels.

quant-ph↗

arXiv2011

Perfect State Transfer in Two and Three Dimensional Structures

We introduce a scheme for perfect state transfer in regular two and three dimensional structures. The interactions on the lattices are of XX spin type with uniform couplings. In two dimensions the structure is a hexagonal lattice and in three dimensions it consists of hexagonal planes joined to each other at arbitrary points. We will show that compared to other schemes, i) much less control is needed for routing, ii) the algebra of global control is quite simple, iii) the same kind of control can upload and download qubit states to or from built-in Read-Write (RW) heads. Pivotal use is made of a quantum switch which we introduce and call it Hadamard switch, since its operation depends on the existence of a Hadamard matrix in four dimensions.

quant-ph↗

arXiv2009

Two-qubit state sharing between N parties using only Bell pairs and Bell-measurement

A quantum protocol for sharing an arbitrary two-qubit state between N parties is introduced. Any of the members, can retrieve the state, only with collaboration of the other parties. We will show that in terms of resources, i.e. the number of classical bits, the number of Bell pairs shared, and also the type of measurements, our protocol is more efficient. For achieving this, we introduce the basic technique of secure passing of an unknown two qubit state among a sequence of parties, none of which can retrieve the state without authorization of the sender and the other members of the group.

quant-ph↗

arXiv2009

A complete characterization of the spectrum of the Kitaev model on spin ladders

We study the Kitaev model on a ladder network and find the complete spectrum of the Hamiltonian in closed form. Closed and manageable forms for all eigenvalues and eigenvectors, allow us to calculate the partition function and averages of non-local operators in addition to the reduced density matrices of different subsystems at arbitrary temperatures. It is also briefly discussed how these considerations can be generalized to more general lattices, including three-leg ladders and two dimensional square lattices.

quant-ph↗

arXiv2009

New Phase Transitions in Optimal States for Memory Channels

We investigate the question of optimal input ensembles for memory channels and construct a rather large class of Pauli channels with correlated noise which can be studied analytically with regard to the entanglement of their optimal input ensembles. In a more detailed study of a subclass of these channels, the complete phase diagram of the two-qubit channel, which shows three distinct phases is obtained. While increasing the correlation generally changes the optimal state from separable to maximally entangled states, this is done via an intermediate region where both separable and maximally entangled states are optimal. A more concrete model, based on random rotations of the error operators which mimic the behavior of this subclass of channels is also presented.

quant-ph↗

arXiv2008

The matrix product representations for all valence bond states

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence-bond states proposed in the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest neighbor interactions, and the partially dimerized or AKLT/VBS (Valence Bond Solid) states, which are constructed from them by projection. The latter states are translation-invariant ground states of Hamiltonians with nearest-neighbor interactions.

quant-ph↗

arXiv2007

Transfer of d-Level quantum states through spin chains by random swapping

We generalize an already proposed protocol for quantum state transfer to spin chains of arbitrary spin. An arbitrary unknown $d-$ level state is transferred through a chain with rather good fidelity by the natural dynamics of the chain. We compare the performance of this protocol for various values of $d$. A by-product of our study is a much simpler method for picking up the state at the destination as compared with the one proposed previously. We also discuss entanglement distribution through such chains and show that the quality of entanglement transition increases with the number of levels $d$.

quant-ph↗

arXiv2005

Equi-entangled bases in arbitrary dimensions

For the space of two identical systems of arbitrary dimensions, we introduce a continuous family of bases with the following properties: i) the bases are orthonormal, ii) in each basis, all the states have the same values of entanglement, and iii) they continuously interpolate between the product basis and the maximally entangled basis. The states thus constructed may find applications in many areas related to quantum information science including quantum cryptography, optimal Bell tests and investigation of enhancement of channel capacity due to entanglement.

quant-ph↗

arXiv2005

Thermal effects on quantum communication through spin chains

We study the effect of thermal fluctuations in a recently proposed protocol for transmission of unknown quantum states through quantum spin chains. We develop a low temperature expansion for general spin chains. We then apply this formalism to study exactly thermal effects on short spin chains of four spins. We show that optimal times for extraction of output states are almost independent of the temperature which lowers only the fidelity of the channel. Moreover we show that thermal effects are smaller in the anti-ferromagnetic chains than the ferromagnetic ones.

quant-ph↗

arXiv2004

Exact solutions for universal holonomic quantum gates

We show how one can implement any local quantum gate on specific qubits in an array of qubits by carrying adiabatically a Hamiltonian around a closed loop. We find the exact form of the loop and the Hamiltonian for implementing general one and two qubits gates. Our method is analytical and is not based on numerical search in the space of all loops.

quant-ph↗