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Quantum Estimation in Open Systems
, Ph.D. Dissertation Sharif University of Technology ; Karimipour, Vahid (Supervisor)
Abstract
In this thesis, we investigate the problem of quantum estimation in open quantum sys- tems. To this end, after a review of classical and quantum estimation theory, and the role of different properties of the quantum systems in enhancing estimation of the closed systems, we will study different characteristics of the open systems. Non-Markovianity of a dynamics is a quantum property which is a special feature of open systems dynamics. It is expected that this property plays a role in the precession of the estimation. Since there is no universal measure for distinguishing Markovian and non-Markovian dynamics, we first use quantum discord between the system and the environment as a measure for...
Characterization of qutrit channels in terms of their covariance and symmetry properties
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 84, Issue 1 , July , 2011 ; 10502947 (ISSN) ; Mani, A ; Memarzadeh, L ; Sharif University of Technology
2011
Abstract
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
Kitaev-Ising model and the transition between topological and ferromagnetic order
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 87, Issue 3 , March , 2013 ; 10502947 (ISSN) ; Memarzadeh, L ; Zarkeshian, P ; Sharif University of Technology
2013
Abstract
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, on 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 two-dimensional Ising model in transverse field, where it shows a transition at a finite value of λ....
Noise effects in perfect transmission of quantum states
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 86, Issue 6 , October , 2012 ; 10502947 (ISSN) ; Floreanini, R ; Karimipour, V ; Sharif University of Technology
2012
Abstract
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 uncorrelated and correlated noise in the external control are studied, and it is remarkably found that the efficiency of the protocol is much higher in the presence of correlated noise
Topological Quantum Computation and the Stability of Topological Memories
, Ph.D. Dissertation Sharif University of Technology ; Karimipour, Vahid (Supervisor)
Abstract
antum computers are necessary to simulate quantum systems. e fragility of qubits in presence of decoherence and external noise is the biggest obstacle in realizing a quantum computer. To overcome su problems, topological quantum computation has been introduced by Kitaev that combines the main quantum feature of the quantum world, namely, superposition of states, with the robustness of classical bits whi is the result of a macroscopic number of very small entities, comprising ea bit. In this way, topological features whi are robust against local perturbations are used for storing information. Kitaev’s model is a famous many-body model, whi has topologically degenerate ground states,...
Time Independent Quantum Circuits with Local Interactions
, M.Sc. Thesis Sharif University of Technology ; Karimipour, Vahid (Supervisor)
Abstract
one of the important challenges for implementation of Quantum Computation is fabrication of Quantum Wires that transport the Quantum Information from one part of the Quantum Hardware to the other parts. Heisenberg Spin Chains are promising candidate for this. In article [28] Gaussian wave packets on the spin chains are used to encode the logical qubits. In this model, to implement unitary operation on these qubits, extra interaction are designed in some parts of the spin chains. As Gaussian wave packets move along this interactions, the desired unitary operators act on them. In fact, this is an static model without external control to perform Quantum Computation. In spite of many interesting...
New phase transitions in optimal states for memory channels
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 79, Issue 3 , 2009 ; 10502947 (ISSN) ; Meghdadi, Z ; Memarzadeh, L ; Sharif University of Technology
2009
Abstract
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...
Sequentially generated entanglement, macroscopicity, and squeezing in a spin chain
, Article Physical Review A ; Volume 96, Issue 4 , 2017 ; 24699926 (ISSN) ; Mølmer, K ; Karimipour, V ; Sharif University of Technology
2017
Abstract
We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a matrix product state (MPS) with the same virtual dimension as the spin qubits. We employ the explicit form of the MPS to calculate expectation values and two-site correlation functions of local observables, and we use the results to study fluctuations of collective observables. Through the so-called macroscopicity and the squeezing properties of the collective spin variables they witness the quantum correlations and multiparticle entanglement within the...
Power of a shared singlet state in comparison to a shared reference frame
, Article Physical Review A ; Volume 100, Issue 2 , 2019 ; 24699926 (ISSN) ; Mani, A ; Karimipour, V ; Sharif University of Technology
American Physical Society
2019
Abstract
We show that a shared singlet state (SSS) can supersede a shared reference frame (SRF) in certain quantum communication tasks, i.e., tasks in which two remote players are required to estimate certain parameters of a two-particle state sent to them. This shows that task-specific values of resources may be somewhat different from their common values based on their exchange possibilities. © 2019 American Physical Society. ©2019 American Physical Society
Entanglement-assisted communication in the absence of shared reference frame
, Article Physical Review A ; Volume 99, Issue 4 , 2019 ; 24699926 (ISSN) ; Raeisi, S ; Karimipour, V ; Sharif University of Technology
American Physical Society
2019
Abstract
Alice wants to convey the value of a parameter to Bob with whom she does not share a reference frame. What physical object can she use for this task? Shall she encode this value into the angle between two physical vectors such as the angle between two spins? Can she benefit from using entanglement? We investigate these questions here and show that an entangled state of two qubits has three parameters that are invariant under changes of the reference frame. We also calculate for specific examples the average information gain for different circumstances, where one of these parameters is used for communication. We compare our result with the special case of separable states and find that...
Quasi-inversion of qubit channels
, Article Physical Review A ; Volume 101, Issue 3 , 2020 ; Benatti, F ; Floreanini, R ; Sharif University of Technology
American Physical Society
2020
Abstract
In general quantum operations, or quantum channels cannot be inverted by physical operations, i.e., by completely positive trace-preserving maps. An arbitrary state passing through a quantum channel loses its fidelity with the input. Given a quantum channel E, we discuss the concept of its quasi-inverse as a completely positive trace-preserving map Eqi which when composed with E increases its average input-output fidelity in an optimal way. The channel Eqi comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples. © 2020 American Physical Society
Secure alignment of coordinate systems using quantum correlation
, Article Physical Review A ; Volume 96, Issue 2 , 2017 ; 24699926 (ISSN) ; Mani, A ; Karimipour, V ; Sharif University of Technology
2017
Abstract
We show that two parties far apart can use shared entangled states and classical communication to align their coordinate systems with a very high fidelity. Moreover, compared with previous methods proposed for such a task, i.e., sending parallel or antiparallel pairs or groups of spin states, our method has the extra advantages of using single-qubit measurements and also being secure, so that third parties do not extract any information about the aligned coordinate system established between the two parties. The latter property is important in many other quantum information protocols in which measurements inevitably play a significant role. © 2017 American Physical Society
Computing on quantum shared secrets for general quantum access structures
, Article Quantum Information Processing ; Volume 18, Issue 4 , 2019 ; 15700755 (ISSN) ; Boreiri, S ; Karimipour, V ; Sharif University of Technology
Springer New York LLC
2019
Abstract
Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this paper, we first propose a method for sharing a quantum secret in a basic (2, 3) threshold scheme, only by using qubits and the 7-qubit CSS code. Based on this (2, 3) scheme, we propose a new (n, n) scheme, and we also construct a quantum secret sharing scheme for any quantum access structure by induction. Secondly, based on the techniques of performing quantum computation on 7-qubit CSS codes, we introduce a method that authorized subsets can perform...
Quantum key distribution with no shared reference frame
, Article Quantum Information Processing ; Volume 19, Issue 2 , 2020 ; Mani, A ; Karimipour, V ; Sharif University of Technology
Springer
2020
Abstract
Any quantum communication task requires a common reference frame (i.e., phase, coordinate system). In particular, quantum key distribution requires different bases for preparation and measurements of states which are obviously based on the existence of a common frame of reference. Here, we show how QKD can be achieved in the absence of any common frame of reference. We study the coordinate reference frame, where the two parties do not even share a single direction, but the method can be generalized to other general frames of reference, pertaining to other groups of transformations. © 2019, Springer Science+Business Media, LLC, part of Springer Nature
Matrix product representations for spin-(1/2) and spin-(3/2) spontaneous quantum ferrimagnets
, Article EPL ; Volume 84, Issue 6 , January , 2008 ; 02955075 (ISSN) ; Baghbanzadeh, S ; Karimipour, V ; Sharif University of Technology
2008
Abstract
Using the matrix product formalism, we find exact ground states for two new spin-(1/2) and spin-(3/2) quantum chains. On a lattice of 3N sites, these ground states have a total spin of N/2, and hence have ferrimagnetic character. The novel point of this construction is that we construct a matrix product representation, not for a state which is invariant under rotation as has been hitherto considered, but for a state which transforms to other states under this symmetry operation. The method can be directly generalized to other symmetry groups. © Europhysics Letters Association
A new class of models for surface relaxation with exact stationary measures
, Article Europhysics Letters ; Volume 57, Issue 5 , 2002 , Pages 658-664 ; 02955075 (ISSN) ; Seradjeh, S. B. H ; Sharif University of Technology
2002
Abstract
We introduce a class of discrete models for surface relaxation, in which the rates of transitions of particles between adjacent sites depend on the number of particles already present in both the source and target sites. We obtain the exact steady state of the stochastic dynamics in the form of a product measure and calculate various properties of surface including its roughness
Quantum key distribution for d-level systems with generalized Bell states
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 65, Issue 5 , 2002 , Pages 7- ; 10502947 (ISSN) ; Bahraminasab, A ; Bagherinezhad, S ; Sharif University of Technology
2002
Abstract
Using the generalized Bell states and controlled-NOT gates, we introduce an entanglement-based quantum key distribution (QKD) of d-level states (qudits). In case of eavesdropping, Eve’s information gain is zero and a quantum error rate of [Formula Presented] is introduced in Bob’s received qudits, so that for large d, comparison of only a tiny fraction of received qudits with the sent ones can detect the presence of Eve. © 2002 The American Physical Society
Entanglement swapping of generalized cat states and secret sharing
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 65, Issue 4 , 2002 , Pages 5- ; 10502947 (ISSN) ; Bahraminasab, A ; Bagherinezhad, S ; Sharif University of Technology
2002
Abstract
We introduce generalized cat states for d-level systems and obtain concise formulas for their entanglement swapping with generalized Bell states. We then use this to provide both a generalization to the d-level case and a transparent proof of validity for an already proposed protocol of secret sharing based on entanglement swapping. © 2002 The American Physical Society
Quantum key distribution for d-level systems with generalized bell states
, Article Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 65, Issue 5 A , 2002 , Pages 523311-523317 ; 10502947 (ISSN) ; Bahraminasab, A ; Bagherinezhad, S ; Sharif University of Technology
American Physical Society
2002
Abstract
An entanglement-based quantum key distribution (QKD) of d-level states was presented. The generalized Bell states and controlled-NOT gates were used for this purpose. The security of the QKD against some individual attacks was discussed. The consequences of replacing the Hadamard gates with an arbitrary unitary gate were also investigated
Entanglement swapping of generalized cat states and secret sharing
, Article Physical Review A. Atomic, Molecular, and Optical Physics ; Volume 65, Issue 4 A , 2002 , Pages 423201-423205 ; 10502947 (ISSN) ; Bahraminasab, A ; Bagherinezhad, S ; Sharif University of Technology
American Institute of Physics Inc
2002
Abstract
The generalized cat states for d-level systems and formula for their entanglement swapping (ES) with the generalized Bell states was discussed. Simple graphical rules for ES of d-level Bell and cat states were derived. A generalization to the d-level case and a transparent proof of validity for protocol of secret sharing based on ES was provided