scholarly journals Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Paul B. Slater ◽  
Charles F. Dunkl
Keyword(s):  
Hypergeometric Function ◽  
High Precision ◽  
Quantum States ◽  
Approximation Procedure ◽  
Density Approximation ◽  
Density Matrices ◽  
Qubit States ◽  
Induced Measure

Previously, a formula, incorporating a5F4hypergeometric function, for the Hilbert-Schmidt-averaged determinantal momentsρPTnρk/ρkof4×4density-matrices (ρ) and their partial transposes (|ρPT|), was applied withk=0to the generalized two-qubit separability probability question. The formula can, furthermore, be viewed, as we note here, as an averaging over “induced measures in the space of mixed quantum states.” The associated induced-measure separability probabilities (k=1,2,…) are found—viaa high-precision density approximation procedure—to assume interesting, relatively simple rational values in the two-re[al]bit (α=1/2), (standard) two-qubit (α=1), and two-quater[nionic]bit (α=2) cases. We deduce rather simple companion (rebit, qubit, quaterbit, …) formulas that successfully reproduce the rational values assumed forgeneral  k. These formulas are observed to share certain features, possibly allowing them to be incorporated into a single master formula.

Symmetric and asymmetric cyclic controlled quantum teleportation via nine-qubit entangled state

2021 ◽  
pp. 2150249
Author(s):  
Vikram Verma
Keyword(s):  
Quantum Channel ◽  
Quantum Teleportation ◽  
Quantum States ◽  
Entangled State ◽  
Controlled Quantum Teleportation ◽  
Intrinsic Efficiency ◽  
Qubit States ◽  
Generalized Scheme

In this paper, by utilizing a nine-qubit entangled state as a quantum channel, we propose new schemes for symmetric and asymmetric cyclic controlled quantum teleportation (CYCQT). In our proposed schemes, four participants Alice, Bob, Charlie and David teleport their unknown quantum states cyclically among themselves with the help of a controller Eve. No participants can reconstruct the original states sent from the respective senders without the permission of the controller. Also, by considering same nine-qubit entangled state as a quantum channel, we propose a generalized scheme for CYCQT of multi-qubit states. In contrast to the previous CYCQT schemes involving three communicators and a controller, there are four communicators and a controller in the proposed schemes. Also, compared with previous CYCQT schemes, our proposed CYCQT schemes require less consumption of quantum resource and the intrinsic efficiency of the generalized scheme increases with the increase of number of qubits in the information states.

scholarly journals Average of Uncertainty Product for Bounded Observables

2018 ◽  
Vol 25 (02) ◽  
pp. 1850008 ◽  
Author(s):  
Lin Zhang ◽  
Jiamei Wang
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Quantum States ◽  
Density Matrices ◽  
Finite Dimensional ◽  
Uncertainty Product ◽  
Schmidt Norm ◽  
Rank One ◽  
Pure States ◽  
Average Uncertainty

The goal of this paper is to calculate exactly the average of uncertainty product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of pure and isospectral states as well as the states distributed uniformly according to the measure induced by the Hilbert-Schmidt norm. Firstly, we investigate the average uncertainty of an observable over isospectral density matrices. By letting the isospectral density matrices be of rank-one, we get the average uncertainty of an observable restricted to pure quantum states. These results can help us check how large is the gap between the uncertainty product and any lower bounds obtained for the uncertainty product. Although our method in the present paper cannot give a tighter lower bound of uncertainty product for bounded observables, it can help us drop any one that is not substantially tighter than the known one.

scholarly journals Generation and Application of Nested Entanglement in Matryoshka Quantum Resource-States

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Quantum Teleportation ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Bell States ◽  
Controlled Teleportation ◽  
Multipartite Entanglement ◽  
Spin Interaction ◽  
State Generation ◽  
Qubit States ◽  
Resource State

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.

The one-way information deficit for a class of two-qubit states

2015 ◽  
Vol 13 (02) ◽  
pp. 1550012
Author(s):  
H. Eftekhari ◽  
E. Faizi
Keyword(s):  
Dynamic Behavior ◽  
Quantum States ◽  
Parameter Family ◽  
General Quantum ◽  
The One ◽  
Qubit States ◽  
Additional Assumptions ◽  
Explicit Expressions

So far, one-way information deficit (OWID) has been calculated explicitly only for Bell-diagonal states and the four-parameter family of X-states with additional assumptions and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for OWID for a larger class of two-qubit states, namely, a five-parameter family of two-qubit states. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID is more robust against the decoherence than the entanglement.

Security analysis of KXB10 QKD protocol with higher-dimensional quantum states

2021 ◽  
pp. 2150005
Author(s):  
Usama Ahsan ◽  
Muhammad Mubashir Khan ◽  
Asad Arfeen ◽  
Khadija Azam
Keyword(s):  
Quantum Key Distribution ◽  
Security Analysis ◽  
Higher Dimensions ◽  
Transmission Error ◽  
Quantum States ◽  
Higher Dimensional ◽  
Implementation Techniques ◽  
Generalized Dimension ◽  
Secret Keys ◽  
Qubit States

Quantum key distribution (QKD) is one of the exciting applications of quantum mechanics. It allows the sharing of secret keys between two communicating parties with unconditional security. A variety of QKD protocols have been proposed since the inception of the BB84 protocol. Among different implementation techniques of QKD protocols, there is a category which exploits higher dimensions qubit states to encode classical bits. In this paper, we focus on such a QKD protocol called KXB10, which uses three bases with higher dimensions. Analysis of the generalized dimension quantum states is performed by evaluating it based on the index transmission error rate ITER. We find that there is a direct relationship between qubit dimensions and ITER for the KXB10 protocol.

Interference of Quantum States and Superposition Principle in Probability Representation of Quantum Mechanics

2019 ◽  
Vol 26 (03) ◽  
pp. 1950016 ◽  
Author(s):  
Margarita A. Man’ko ◽  
Vladimir I. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distributions ◽  
Superposition Principle ◽  
State Density ◽  
Quantum States ◽  
Density Matrices ◽  
Probability Representation ◽  
Density Operators ◽  
Pure States

The superposition of pure quantum states explicitly expressed in terms of a nonlinear addition rule of state density operators is reviewed. The probability representation of density matrices of qudit states is used to formulate the interference of the states as a combination of the probability distributions describing pure states. The formalism of quantizer–dequantizer operators is developed. Examples of spin-1/2 states and f-oscillator systems are considered.

scholarly journals CHARACTERIZING QUANTUMNESS VIA ENTANGLEMENT CREATION

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1701-1713 ◽  
Author(s):  
SEVAG GHARIBIAN ◽  
MARCO PIANI ◽  
GERARDO ADESSO ◽  
JOHN CALSAMIGLIA ◽  
PAWEŁ HORODECKI
Keyword(s):  
Relative Entropy ◽  
Special Class ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Bipartite Entanglement ◽  
Separable States ◽  
Classical Quantum ◽  
Qubit States

In [Piani et al., PRL106 (2011) 220403], an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical–quantum states. In particular, we fully characterize the classical–quantum two-qubit states that are maximally non-classical.

scholarly journals Algorithmic construction of local models for entangled quantum states: Optimization for two-qubit states

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
Mathieu Fillettaz ◽  
Flavien Hirsch ◽  
Sébastien Designolle ◽  
Nicolas Brunner
Keyword(s):  
Quantum States ◽  
Local Models ◽  
Entangled Quantum States ◽  
Algorithmic Construction ◽  
Qubit States

scholarly journals Condition for zero and nonzero discord in graph Laplacian quantum states

2019 ◽  
Vol 17 (02) ◽  
pp. 1950018 ◽  
Author(s):  
Supriyo Dutta ◽  
Bibhas Adhikari ◽  
Subhashish Banerjee
Keyword(s):  
Quantum Mechanics ◽  
Quantum Discord ◽  
Graph Laplacian ◽  
Quantum Correlations ◽  
Quantum States ◽  
Simple Graphs ◽  
Graph Theoretic ◽  
Weighted Directed Graph ◽  
Special Case ◽  
Qubit States

This work is at the interface of graph theory and quantum mechanics. Quantum correlations epitomize the usefulness of quantum mechanics. Quantum discord is an interesting facet of bipartite quantum correlations. Earlier, it was shown that every combinatorial graph corresponds to quantum states whose characteristics are reflected in the structure of the underlined graph. A number of combinatorial relations between quantum discord and simple graphs were studied. To extend the scope of these studies, we need to generalize the earlier concepts applicable to simple graphs to weighted graphs, corresponding to a diverse class of quantum states. To this effect, we determine the class of quantum states whose density matrix representation can be derived from graph Laplacian matrices associated with a weighted directed graph and call them graph Laplacian quantum states. We find the graph theoretic conditions for zero and nonzero quantum discord for these states. We apply these results on some important pure two qubit states, as well as a number of mixed quantum states, such as the Werner, Isotropic, and [Formula: see text]-states. We also consider graph Laplacian states corresponding to simple graphs as a special case.

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