Quantum mechanics has traditionally relied on entanglement as the primary resource for describing non-classical correlations between distinct physical systems. However, entanglement fails to capture the entirety of mutual information and systemic accessibility, particularly in open, mixed, or high-dimensional environments where local states and shared correlations exhibit distinct scaling behaviors. In this paper, we introduce the concept of Mutual Observability of Quantum States (MOQ), a novel theoretical framework that quantifies how effectively one quantum system can observe or be observed by another, independently of traditional entanglement constraints. We define the mutual observability index V_AB as the ratio of the mutual information I(A:B) to the sum of the local von Neumann entropies S(A) + S(B). Through rigorous mathematical formulation, we establish its strict analytical bounds within the closed interval from 0 to 1, explore its fundamental algebraic properties, and analyze its dynamical behavior in open quantum systems. We demonstrate that MOQ dictates the strength of measurable influence and information transfer between subsystems even when quantum entanglement vanishes entirely. This framework establishes a paradigm shift in understanding quantum correlations, paving the way for advanced applications in quantum communication networks, quantum state estimation, and quantum thermodynamics.
Quantum mechanics has traditionally relied on entanglement as the primary resource for describing non-classical correlations between distinct physical systems. However, entanglement fails to capture the entirety of mutual information and systemic accessibility, particularly in open, mixed, or high-dimensional environments where local states and shared correlations exhibit distinct scaling behaviors. In this paper, we introduce the concept of Mutual Observability of Quantum States (MOQ), a novel theoretical framework that quantifies how effectively one quantum system can observe or be observed by another, independently of traditional entanglement constraints. We define the mutual observability index V_AB as the ratio of the mutual information I(A:B) to the sum of the local von Neumann entropies S(A) + S(B). Through rigorous mathematical formulation, we establish its strict analytical bounds within the closed interval from 0 to 1, explore its fundamental algebraic properties, and analyze its dynamical behavior in open quantum systems. We demonstrate that MOQ dictates the strength of measurable influence and information transfer between subsystems even when quantum entanglement vanishes entirely. This framework establishes a paradigm shift in understanding quantum correlations, paving the way for advanced applications in quantum communication networks, quantum state estimation, and quantum thermodynamics.
Within the framework of Information Theory, the existence of correlations between two random variables means that we can obtain information about one of them, just by measuring or observing the other random variable. In certain cases, this kind of relationship allows obtaining information about a variable even when the other is separated by a very large distance, that is, the process of obtaining information is non-local, an example (if not the only) is the quantum entanglement. These features of correlations make it interesting and important to study, classify and quantify them. The correlations are classified into classical correlations and quantum correlations, in addition they are quantified through the mutual information. Here we will present a natural way to define classical mutual information and then we will generalize it to the quantum case. Furthermore, every term in the definitions of mutual information will be interpreted using the concepts of classical and quantum entropy.
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.
This chapter provides a comprehensive introduction to the foundational concepts and advanced developments of mathematical perspectives on quantum information theory. Beginning with the distinctions between classical and quantum information, we explore key measures of quantum correlations such as entanglement entropy, mutual information, and entanglement of purification. Various entanglement quantifiers – including concurrence and negativity – are discussed in the context of bipartite and mixed states. The chapter also introduces quantum channels, noise models, and their physical realizations in systems ranging from superconducting qubits to black holes. We present key quantum algorithms, including Shor’s factoring algorithm and Grover’s search, along with their underlying principles such as the quantum Fourier transform. Bridging theory and practice, this chapter sets the stage for further exploration into quantum error correction, quantum thermodynamics, and the role of information in fundamental physics. The material is designed to be accessible to graduate students, researchers, and professionals across the disciplines of physics, computer science, and engineering.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, presents a significant challenge to classical physics. While entanglement is undeniably a bizarre and seemingly paradoxical aspect of the quantum world, its implications extend far beyond theoretical curiosity. This paper explores the potential of a novel modeling framework for quantum entanglement, grounded in the principles of non-locality. We propose a dynamic correlation model, parameterized by a "quantum correlation degree," that captures the inherent uncertainty and interconnectedness in entangled states. The framework utilizes a computational approach, specifically leveraging a modified quantum algorithm, to simulate and analyze entangled systems. This work introduces a new perspective on entanglement, moving beyond traditional approaches that primarily focus on local realism. We argue that this framework offers a robust and flexible approach to understanding and potentially manipulating entanglement, opening avenues for novel quantum algorithms and potential advancements in quantum information processing. The core claim is that this model provides a mathematically rigorous, computationally feasible framework for understanding and modeling non-local entanglement.
Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems, but can also be implemented in quantum-optical systems.
The origin of the macroscopic arrow of time remains one of the most profound puzzles in theoretical physics, traditionally tied to the monotonic increase of total entropy dictated by the second law of thermodynamics. In this work, we propose and rigorously analyze the concept of the Quantum Thermodynamic Arrow Inverter (QTAI), a theoretical framework designed within open quantum systems where a local subsystem can exhibit a transient or sustained decrease in local entropy, characterized mathematically by d S_sub / dt < 0, while the global composite system strictly satisfies the global second law of thermodynamics, given by d S_total / dt >= 0. Rather than focusing merely on conventional cooling or refrigeration cycles, QTAI investigates whether the thermodynamic arrow of time can be dynamically and non-trivially redistributed across entangled and correlated quantum sub-degrees of freedom. By leveraging non-Markovian system-environment interactions, quantum coherence, and information-theoretic resource allocation, we demonstrate that different subsystems can effectively experience distinct local temporal directions or asymmetric thermodynamic aging. This paradigm introduces the Arrow of Time Redistribution as a fundamental principle, potentially bridging quantum information theory, open system dynamics, and the foundational nature of time itself.