Sharif Digital Repository

We study four well-known capacities of a two-parameter family of qubit Pauli channels. These are the channels that are covariant under the SO(2) group and contain the depolarizing channel as a special case. We find exact expressions for the classical capacity and entanglement-assisted capacities, and analytically determine the regions where the quantum capacity of the channel vanishes. We then use a flag extension to find upper bound for the quantum capacity and private capacity of these channels in the entire region of parameter space and also obtain the lower bound for the quantum capacity by calculating the single-shot quantum capacity numerically. In conjunction with previous results on... 

Continuous clocks, i.e., clocks that measure time in a continuous manner, are regarded as an essential component of sensing technology. Precision and recurrence time are two basic features of continuous clocks. In this paper, in the framework of quantum estimation theory various models for continuous quantum clocks are proposed, and all tools of quantum estimation theory are employed to seek the characteristics of clocks with high precision and long recurrence time. Then, in a resource-based approach, the performances of the proposed models are compared. It is shown that quantum clocks based on an n two-qubit system not only can have better precision than quantum clocks based on a 2n... 

In this paper, we study non-Gaussian discrete-modulated measurement-deviceindependent continuous-variable quantum key distribution protocol equipped with a proposed quantum scissor at the receiver side. Our suggested scissor truncates all multiphoton number states with four or more photons and amplifies remaining photon number states in a probabilistic way. Using exact non-Gaussian calculation, we find that quantum scissor meliorates the fidelity and entanglement between two legitimate parties Alice and Bob, at long distances. Therefore, quantum scissor enhances the continuous-variable quantum key distribution protocol range. Examination of the system for different values of the excess noise... 

Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging and valuable open problem in quantum information theory. Here we introduce a systematic approach that, despite the lack of knowledge about the full parametrization of the set of CPTP maps on arbitrary Hilbert-spaced dimension, enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme... 

Two qubit density matrices which are of X-shape, are a natural generalization of Bell Diagonal States (BDSs) recently simulated on the IBM quantum device. We generalize the previous results and propose a quantum circuit for simulation of a general two qubit X-state, implement it on the same quantum device, and study its entanglement for several values of the extended parameter space. We also show that their X-shape is approximately robust against noisy quantum gates. To further physically motivate this study, we invoke the two-spin Heisenberg XYZ system and show that for a wide class of initial states, it leads to dynamical density matrices which are X-states. Due to the symmetries of this... 

We study the 3D Kitaev and Kitaev-Heisenberg models, respectively, on the hyperhoneycomb and hyperoctagon lattices, both at zero and finite-temperature, in the thermodynamic limit. Our analysis relies on advanced tensor network (TN) simulations based on graph projected entangled-pair states (gPEPS). We map out the TN phase diagrams of the models and characterize their underlying gapped and gapless phases both at zero and finite temperature. In particular, we demonstrate how cooling down the hyperhoneycomb system from high temperature leads to fractionalization of spins to Majorana fermions and gauge fields that occurs in two separate temperature regimes, leaving their fingerprint on specific... 

One of the most elusive problems in quantum mechanics is the transition between classical and quantum physics. This problem can be traced back to Schrödinger's cat thought experiment. A key element that lies at the center of this problem is the lack of a clear understanding and characterization of macroscopic quantum states. Our understanding of macroscopic quantumness relies on states such as the Greenberger-Horne-Zeilinger (GHZ) or the NOON state. Here we take a first-principle approach to this problem. We start from coherence as the key quantity that captures the notion of quantumness and require the quantumness to be collective and macroscopic. To this end, we introduce macroscopic... 

We investigate the second quantization form of the entanglement Hamiltonian (EH) of various subregions for the ground state of several interacting lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground state of generic local Hamiltonians. In this paper, we demonstrate that the EH is practically local and its dominant components are related to the terms present in the model Hamiltonian up to a smooth spatially varying temperature even for (a) discrete lattice systems, (b) systems with no emergent conformal or Lorentz symmetry, and (c) subsystems with nonflat boundaries, up to relatively strong interactions. We show... 

Barcoding photons, atoms, and any quantum states can provide a host of functionalities that could benefit future quantum communication systems and networks beyond today's imagination. As a significant application of barcoding photons, we introduce code division multiple-access (CDMA) communication systems for various applications. In this context, we introduce and discuss the fundamental principles of a novel quantum CDMA (QCDMA) technique based on spectrally encoding and decoding of continuous-mode quantum light pulses. In particular, we present the mathematical models of various QCDMA modules that are fundamental in describing an ideal and typical QCDMA system, such as quantum signal... 

Correlations disguised in various forms underlie a host of important phenomena in classical and quantum systems, such as information and energy exchanges. The quantum mutual information and the norm of the correlation matrix are both considered as proper measures of total correlations. We demonstrate that, when applied to the same system, these two measures can actually show significantly different behavior except at least in two limiting cases: when there are no correlations and when there is maximal quantum entanglement. We further quantify the discrepancy by providing analytic formulas for time derivatives of the measures for an interacting bipartite system evolving unitarily. We argue... 

We construct a large family of planar maximally entangled (PME) states, which are a wider class of multipartite entangled states than absolutely maximally entangled (AME) states. These are states in which any half of the qudits are in a maximally mixed state, provided that they form a connected subset. We show that in contrast to AMEs, PMEs are easier to find and there are various PMEs for any even number of qudits. In particular, while it is known that no AME state of four qubits exists, we show that there are two distinct multiparameter classes of four-qubit PMEs. We also give explicit families of PMEs for any even number of particles and for any dimension. We also briefly mention the... 

Entangled states can be used as secure carriers of information much in the same way as carriers are used in classical communications. In such protocols, quantum states are uploaded to the carrier at one end and are downloaded from it in safe form at the other end, leaving the carrier intact and ready for reuse. Furthermore, protocols have been designed for performing quantum state sharing in this way. In this work, we study the robustness of these protocols against two of the most common sources of noise, namely de-phasing and depolarization and show that multiple uses of these carriers do not lead to accumulative errors, rather the error remains constant and under control. © 2020, Springer... 

Entanglement is one of the key resources of quantum information science which makes identification of entangled states essential to a wide range of quantum technologies and phenomena. This problem is however both computationally and experimentally challenging. Here we use autoencoder neural networks to find semi-optimal set of incomplete measurements that are most informative for the detection of entangled states. We show that it is possible to find high-performance entanglement detectors with as few as three measurements. Also, with the complete information of the state, we develop a neural network that can identify all two-qubits entangled states almost perfectly. This result paves the way... 

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  

In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the QFI in the sense that two close states with close first derivatives have close QFIs. This property is completely general and irrespective of dynamics or how states acquire their parameter dependence and also the form of parameter dependence-indeed this continuity is basically a feature of the classical Fisher information that in the case of the QFI naturally carries over from the manifold of probability distributions onto the manifold of density matrices. We... 

We present a general graph-based projected entangled-pair state (gPEPS) algorithm to approximate ground states of nearest-neighbor local Hamiltonians on any lattice or graph of infinite size. By introducing the structural matrix, which codifies the details of tensor networks on any graphs in any dimension d, we are able to produce a code that can be essentially launched to simulate any lattice. We further introduce an optimized algorithm to compute simple tensor updates as well as expectation values and correlators with a mean-field-like effective environments. Though not being variational, this strategy allows to cope with PEPS of very large bond dimension (e.g., D=100) and produces... 

The discrete-time quantum walk dynamics can be generated by a time-dependent Hamiltonian, repeatedly switching between the coin and the shift generators. We change the model and consider the case where the Hamiltonian is time-independent, including both the coin and the shift terms in all times. The eigenvalues and the related Bloch vectors for the time-independent Hamiltonian are then compared with the corresponding quantities for the effective Hamiltonian generating the quantum walk dynamics. Restricted to the non-localized initial quantum walk states, we optimize the parameters in the time-independent Hamiltonian such that it generates a dynamics similar to the Hadamard quantum walk. We... 

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... 

We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT), which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibit emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial noninteracting counterpart, and thus is of a pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the... 

This paper is a proposal for the generation of a many-body entangled state in atomic and mechanical systems. Here the detailed feasibility study shows that application of a strong Rydberg dressing interaction and a fast bifurcation scheme in a Bose-Einstein condensate of Rb atoms, results in the formation of large cat states. By detailed study of the decoherence effects using the quantum jump Monte Carlo approach and taking into account the obstacles like collective decoherence and level mixing, this proposal predicts the formation of a 700-atom cat state. Subsequent transfer of the generated superposition to far separated mechanical oscillators is proposed, using dipole coupling between...