Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer
Elias Riedel Gårding, Nicolas Schwaller, Chun Lam Chan, Su Yeon Chang, Samuel Bosch, Frédéric Gessler, Willy Robert Laborde, Javier Naya Hernández, Xinyu Si, M.‐A. Dupertuis, Nicolas Macris
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between "quantum discord" and "asymmetric relative entropy of discord": the former never exceeds the latter. We also prove that for all BDS the two coincide.
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between "quantum discord" and "asymmetric relative entropy of discord": the former never exceeds the latter. We also prove that for all BDS the two coincide.
We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell diagonal states is generated, and several characteristic indicators, namely entanglement of formation and concurrence, CHSH non-locality, steering and discord, are experimentally evaluated over the full parameter space and compared with theory. As a by-product of this work, we also find a remarkable general inequality between “quantum discord” and “asymmetric relative entropy of discord”: the former never exceeds the latter. We also prove that for all BDS the two coincide.
Bell-diagonal states are extremely important for understanding the dynamics and applications of some quantum resources. Quantum properties such as steering, entanglement, and coherence, among others, can be used as resources in quantum computing. Because of this, we believe it is necessary to understand the preparation of these states. We create an adjustable quantum circuit, which we implement on the International Business Machines (IBM) quantum computer. These computers are an excellent possibility for carrying out experiments like this. We implement the circuit on three different quantum chips that are available on the online platform. As an example, we measure non-locality, steering, entanglement, discord and non-local coherence for Werner states, which are a special type of the Bell-diagonal. We compare the theoretical results with the experimental data. We note the harmful effect that noise can have on quantum circuits, bringing undesirable decoherence effects to the system. We model noise in a simple way, using two quantum channels, amplitude damping and phase damping. We investigate the direct relationship between measures of discord and entanglement, as well as the sudden change of discord. But, even carrying out these tests on several quantum chips, it was not possible to carry out such verification with great clarity. On the other hand, the great importance of Bohr’s Complementarity Principle for Quantum Mechanics is well known. However, the search for quantifiers to measure wave or particle characteristics, in a quantum system, has always been very intense. Recently, a formalism was developed based on basic properties of the density matrix ( 0; Tr = 1). We use the IBM quantum computer to check the complementarity relationships based on these properties. We calculate quantum coherence, predictability and quantum correlations for a particular class of quantum states of one qubit and also for random quantum states of one, two and three qubits. We note that for both cases, the interaction of the system with the environment, and the consequent creation of correlation, generates a decrease in the sum of quantum coherence and predictability but which is compensated by the increase in quantum correlations between system and environment.
Quantum states can be correlated in ways beyond what is possible for classical states. These correlations are considered as the main resource for quantum computation and communication tasks. In this thesis, I present my studies on the different forms of Quantum Correlations known as "Quantum Discord", "Einstein-Podolsky-Rosen(EPR) Steering" and "Bel-type correlations" in the continuous-variable quantum states and investigate their practical applications for the secure quantum communication. While previously quantum entanglement was considered as the only form of quantum correlation, in the recent years a notion known as quantum discord which captures extra quantum correlations beyond entanglement was introduced by Ollivier and Zurek. This sort of non-classicality that can exist even in separable states, has raised so much aspiration for the potential applications, as they are less fragile than the entangled states. Therefore, of especial interest is to know if a bipartite quantum state is discordant or not. In this thesis I will describe the simple and efficient experimental technique that we have introduced and experimentally implemented to verify quantum discord in unknown Gaussian states and a certain class of non-Gaussian states. According to our method, the peak separation between the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurement conducted on the other subsystem is an indication of nonzero quantum discord. We implemented this method experimentally by preparing bipartite Gaussian and non-Gaussian states and proved nonzero quantum discord in all the prepared states. Though quantum key distribution has become a mature technology, the possibility of hacking the devices used in the quantum communications has motivated the scientists to develop the schemes where one or non of the devices used by the communicating parties need to be trusted. Quantum correlations are the key to develop these schemes. Particularly, EPR steering is connected to the one-sided-deviceindependent quantum key distribution in which devices of one party are solely trusted and Bell-type correlations to the fully device-independent quantum key distribution where non of the apparatuses of the communicating parties is trusted. Here, I will present the result of our theoretical and experimental research to develop one-sided-device-independent quantum key distribution in continuous variables. We identify all Gaussian protocols that can in principle be one-sided-device independent. This consists of 6 protocols out of 16 possible Gaussian protocols, which surprisingly includes the protocol that applies only coherent states. We experimentally implemented both the entanglement-based and coherent state protocols and manifested their loss tolerance. Our results open the door for the practical secure quantum communications, asserting the link between the EPR-steering andone-sided-device-independence. Due to the maturity of quantum information using continuous variables, it is important to develop a Bell-type inequality in this regime. Despite its fundamental importance, Bell-type correlation is linked to the device-independent quantum key distribution. I developed a computer modelling based on the proposal of ref [1, 2] to demonstrate continuous-variable Bell-type correlation. The results of my computer simulations that are presented in this thesis show the feasibility of these proposals, which makes the real-life implementation of continuous-variable device-independent quantum key distribution possible.
Abstract Quantum key distribution (QKD) facilitates secure communication by harnessing non-classical correlations within quantum systems. Although entanglement is fundamental to many QKD protocols, it is highly susceptible to noise and decoherence effects. In this work, we analyze the performance of Werner and Bell-diagonal states within commonly used QKD protocols such as BB84, Six-state, and their device-independent variants, considering realistic noise environments and eavesdropping strategies. Employing a Qiskit-based simulation toolkit , we assess critical performance metrics including quantum bit error rate (QBER), fidelity, concurrence, quantum discord, violations of the CHSH inequality, and Devetak, Winter key rates. Our findings emphasize the resilience of quantum discord as a resource in scenarios where entanglement is diminished, and reveal that Bell-diagonal states may exhibit superior performance compared to Werner states under certain noise conditions. We further discuss practical consequences for secure key generation and propose directions for extending this work toward physical device implementation and machine learning–enhanced detection of eavesdropping attempts. These results shed light on the robustness of QKD protocols that utilize mixed quantum states and the significant role quantum discord can play in secure quantum communication.
Quantum discord is a measure of nonclassical correlations in quantum systems. While the bipartite version of quantum discord is experimentally well-studied, the multipartite version has never been convincingly measured. In this study, we experimentally investigate tripartite quantum discord using an NMR quantum information processor. Building on a theoretical framework for conditional projective measurements and quantum conditional mutual information, we quantify the tripartite quantum discord and its contributions in different three-qubit states such as the Greenberger-Horne-Zeilinger (GHZ) and Werner (W) states as well as classical mixtures of biseparable Bell states, and classical mixtures of product states. The experiments employed full quantum state tomography and temporal averaging to prepare mixed states, achieving fidelities exceeding 95%. Our results confirm that quantum discord persists even in the absence of entanglement, highlighting its utility as a broader indicator of quantum correlations. Furthermore, we validate the nonconvexity of discord, confirming that classical mixtures of zero-discord states can exhibit nonzero discord. This experimentally confirms that quantum discord does not fit into the framework of resource theory. This work establishes a robust methodology for measuring quantum discord, illuminating the structure and distribution of quantum correlations in multipartite systems.
Abstract Quantum teleportation fundamentally depends on shared quantum correlations between spatially separated parties. Although entanglement is widely recognized as the primary resource enabling teleportation, quantum discord represents a more general form of nonclassical correlations that can persist even when entanglement is absent. We provide a thorough analysis combining analytical and numerical evaluations of quantum discord, negativity, and concurrence across varying noise parameters. The study includes simulations under both ide-alized and realistic noisy conditions, incorporating depolarizing noise models alongside experimentally relevant constraints. To improve quantum fidelity and accurately characterize quantum correlations in noisy environments, advanced error mitigation techniques—such as measurement error correction and zero-noise extrapolation—are applied. In this study, we focus on teleportation protocols utilizing two-qubit Werner states, which constitute a significant class of noisy mixed states modeling imperfect entanglement. We systematically examine how the teleportation fidelity varies as a function of the Werner mixing parameter λ and investigate its relationship with the corresponding quantum discord. Our findings indicate that quantum discord remains strictly greater than zero even in parameter regions where entanglement vanishes, emphasizing the role of discord in sustaining quantum advantages in teleportation schemes exposed to noise and imperfections. This highlights the importance of considering non-entanglement quantum correlations for a comprehensive understanding of teleportation resources in realistic settings.