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Quantum Theory and Quantum Entanglement: A Review of Quantum Correlations

Sakshi Jangid, Nasreen Ansari

Published Jun 1, 2026• 0 citations
Publisher

Abstract

The most common type of quantum correlations is quantum entanglement, which plays an indisputable vital role in a number of quantum information theory tasks, including quantum teleportation, quantum dense coding, and quantum cryptography. However, current findings indicate that different Entanglement is not necessary for applications in quantum information theory, and their performance can be described by a novel kind of quantum correlations that transcends entanglement. The most well-liked candidate for such widespread quantum connections is quantum discord, which Zurek first proposed more than ten years ago. We provide an overview of this current line of inquiry in this work. Following a brief overview of the fundamental ideas of quantum theory and entanglement, we introduce quantum discord and generic quantum correlations and go over three applications that are predicated on this novel kind of correlation: transmission of correlations, entanglement dispersion, and remote state preparation. We also provide an outlook for future research in this area.

DOI
10.5281/zenodo.20518875

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The most common type of quantum correlations is quantum entanglement, which plays an indisputable vital role in a number of quantum information theory tasks, including quantum teleportation, quantum dense coding, and quantum cryptography. However, current findings indicate that different Entanglement is not necessary for applications in quantum information theory, and their performance can be described by a novel kind of quantum correlations that transcends entanglement. The most well-liked candidate for such widespread quantum connections is quantum discord, which Zurek first proposed more than ten years ago. We provide an overview of this current line of inquiry in this work. Following a brief overview of the fundamental ideas of quantum theory and entanglement, we introduce quantum discord and generic quantum correlations and go over three applications that are predicated on this novel kind of correlation: transmission of correlations, entanglement dispersion, and remote state preparation. We also provide an outlook for future research in this area.
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Quantum entanglement is the most popular kind of quantum correlations. Its role in several tasks in quantum information theory like quantum cryptography, quantum dense coding and quantum teleportation is indisputable. The role of entanglement in quantum algorithms has also attracted enormous amount of attention in the literature. The research in this direction is motivated by the finding that a quantum computer can efficiently factorize arbitrary integer numbers. Since no classical algorithm is known today that can solve this problem efficiently, this example clearly demonstrates the superiority of a quantum computer compared to its classical counterpart. In this context, entanglement also plays a crucial role: if the quantum computer operates on a pure state without entanglement, then the computational process can be simulated efficiently on a classical computer. In this case entanglement is the key ingredient that makes the difference between a quantum and a classical computer. However, the situation is more involved if the computational process is not perfect. In this case the quantum computer operates on a mixed state, and the role of entanglement is less obvious. A seminal result in this direction is a quantum algorithm known under the acronym DQC1. This algorithm operates on an almost maximally mixed state with vanishingly little entanglement. However, DQC1 can still perform tasks efficiently for which no efficient classical algorithm is known today. Thus, it is reasonable to assume that entanglement in general is not related to the efficiency of a quantum algorithm. Triggered by this observation other kinds of quantum correlations have been studied. In this context a particular measure of quantum correlations known as quantum discord is referred to frequently in the literature. Quantum discord is a measure of quantum correlations beyond entanglement, i.e., a quantum state can have no entanglement, but nonvanishing quantum discord. Quantum discord is also regarded as the key resource in the DQC1 algorithm. Although this statement is still controversial, it was shown under very general assumptions that quantum discord is required if a quantum computer is to show an exponential speedup over any classical algorithm. In this thesis we give a short introduction into the theory of entanglement and general quantum correlations, and further discuss our results. In particular, we show that two different kinds of entanglement measures can coincide. This result is used to build an algorithm for computing entanglement. We also consider the role of quantum correlations for the distribution of entanglement and for the quantum measurement process. We further discuss the behavior of quantum correlations under local noise, and their monogamy properties.
Quantum entanglement is the most famous type of quantum correlation between elements of a quantum system that has a basic role in quantum communication protocols like quantum cryptography, teleportation and Bell inequality detection. However, it has already been shown that various applications in quantum information theory do not require entanglement. Quantum discord as a new kind of quantum correlations beyond entanglement, is the most popular candidate for general quantum correlations. In this paper, first we find the entanglement witness in a particular multipartite quantum system which consists of a N -partite system in 2 n -dimensional space. Then we give an exact analytical formula for the quantum discord of this system. At the end of the paper, we investigate the additivity relation of the quantum correlation and show that this relation is satisfied for a N -partite system with 2 n -dimensional space.
Abstract Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations (QCs) in composite states. We focus on various approaches to define and quantify general QCs, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.
Quantum entanglement stands as one of the most intriguing phenomena in quantum mechanics, defying classical intuition and paving the way for revolutionary advancements in information processing. the fundamentals of quantum entanglement and explores its applications in quantum information processing. Beginning with a concise overview of entanglement theory, we delve into various protocols and techniques that leverage entangled states to perform tasks such as quantum teleportation, superdense coding, and quantum cryptography. Furthermore, we discuss recent developments in the field, including entanglement-based quantum key distribution schemes and entanglement swapping protocols. Through a comprehensive examination of both theoretical principles and experimental implementations, this paper elucidates the pivotal role of quantum entanglement in shaping the landscape of quantum information processing, with implications for secure communication, computational speedup, and future quantum technologies.