This work studies how measurement type affects information extraction in entangled quantum systems. Local measurements probe subsystems individually, while entangled measurements access global correlations. Information is quantified using Shannon and Rényi entropy. Bell states are used as a baseline, and the analysis is extended to GHZ and W states for systems of up to five qubits. Decoherence is introduced by suppressing phase coherence in the density matrix. The results show that entangled measurements provide maximal information in coherent systems but lose this advantage with decoherence. GHZ states exhibit system-size independent behavior, while W states depend on the number of qubits and display a peak in entropy at intermediate decoherence. This highlights the importance of entanglement structure in determining how information behaves in quantum systems.
This work studies how measurement type affects information extraction in entangled quantum systems. Local measurements probe subsystems individually, while entangled measurements access global correlations. Information is quantified using Shannon and Rényi entropy. Bell states are used as a baseline, and the analysis is extended to GHZ and W states for systems of up to five qubits. Decoherence is introduced by suppressing phase coherence in the density matrix. The results show that entangled measurements provide maximal information in coherent systems but lose this advantage with decoherence. GHZ states exhibit system-size independent behavior, while W states depend on the number of qubits and display a peak in entropy at intermediate decoherence. This highlights the importance of entanglement structure in determining how information behaves in quantum systems.
Abstract In most scenarios, particularly when quantum systems are measured to extract information, W states demonstrate greater robustness compared to Greenberger–Horne–Zeilinger (GHZ) states. This study investigates the evolution of entanglement properties in multi-qubit W and GHZ states under continuous measurement. Our findings reveal that, under specific conditions, GHZ states can exhibit superior entanglement properties relative to W states when qubits are measured using a measurement operator. For the three-qubit case, the GHZ state demonstrates stronger entanglement when all three qubits are measured simultaneously. In the four-qubit scenario, the post-measurement entanglement of the GHZ state surpasses that of the W state when the two central qubits are measured simultaneously. Similarly, for the five-qubit system, the GHZ state achieves higher entanglement than the W state when the three central qubits are measured. Furthermore, as the number of qubits increases, the entanglement between qubits in both GHZ and W states diminishes after measurement.
In this chapter, we discuss several information measures that are important for quantifying the amount of information and correlations that are present in quantum systems. The first fundamental measure that we introduce is the von Neumann entropy (or simply quantum entropy ). It is the quantum generalization of the Shannon entropy, but it captures both classical and quantum uncertainty in a quantum state.1 The quantum entropy gives meaning to the notion of an information qubit . This notion is different from that of the physical qubit, which is the description of a quantum state of an electron or a photon. The information qubit is the fundamental quantum informational unit of measure, determining how much quantum information is present in a quantum system. The initial definitions here are analogous to the classical definitions of entropy, but we soon discover a radical departure from the intuitive classical notions from the previous chapter: the conditional quantum entropy can be negative for certain quantum states. In the classical world, this negativity simply does not occur, but it takes on a special meaning in quantum information theory. Pure quantum states that are entangled have stronger-than-classical correlations and are examples of states that have negative conditional entropy. The negative of the conditional quantum entropy is so important in quantum information theory that we even have a special name for it: the coherent information. We discover that the coherent information obeys a quantum data-processing inequality, placing it on a firm footing as a particular informational measure of quantum correlations. We then define several other quantum information measures, such as quantum mutual information, that bear similar definitions as in the classical world, but with Shannon entropies replaced with quantum entropies. This replacement may seem to make quantum entropy somewhat trivial on the surface, but a simple calculation reveals that a maximally entangled state on two qubits registers two bits of quantum mutual information (recall that the largest the mutual information can be in the classical world is one bit for the case of two maximally correlated bits). We then discuss several entropy inequalities that play an important role in quantum information processing: the monotonicity of quantum relative entropy, strong subadditivity, the quantum data-processing inequalities, and continuity of quantum entropy.
Quantum entanglement is a central resource for quantum computation and state transfer, yet the usefulness of multipartite entanglement depends on how rapidly coherence and nonclassical correlations degrade as the register size and communication depth increase. This methodology paper develops a reproducible density-matrix simulation for studying entanglement and information transfer in multi-qubit systems. GHZ and W states containing 3, 4, 5, 6 and 8 qubits are generated and exposed to independent local depolarizing noise. State fidelity and bipartite negativity are used to quantify preservation of the prepared resource, while an entanglement-assisted multi-hop teleportation model measures the fidelity of transferred single-qubit information. The simulation shows a systematic decrease in state fidelity and negativity with increasing register size at a fixed local error probability. At a local depolarizing probability of 0.02, GHZ fidelity decreases from 0.941 for three qubits to 0.852 for eight qubits, whereas W-state fidelity decreases from 0.943 to 0.877. In a separate transfer experiment with an effective error probability of 0.10 per teleportation hop, average transfer fidelity decreases from 0.933 after one hop to 0.745 after five hops, while remaining above the classical benchmark of 2/3. These results illustrate how multipartite entanglement quality; noise accumulation and path depth jointly determine the reliability of information transfer in multi-qubit computing architectures.
The paper is an elaborate comparative assessment of the most relevant entropy-based quantities to be applied in quantifying quantum entanglement in pure, mixed, bipartite, and multipartite quantum systems. The study fills the existing gap in the literature in which most of the previous literature examines individual measures, but a lot of knowledge is lacking on what these measures are regarding their strengths, weaknesses, and the operational usefulness against each other. The study can prove the behaviour of each measure under noise, decoherence, dimensional scaling, and variation of state-type by analysing von Neumann entropy, the Tsallis entropy, entropy of entanglement of formation, concurrence and logarithmic negativity. Numerical studies with pure two-qubit states, Werner states, GHZ states, W states and mixed random states demonstrate specific sensitivity properties and computational limitations which ensure that no single measure can be a universal quantifier. The paper goes on to say that entropy-only measures do not work in mixed regimes because of a dominance in classical correlations. The results have several important implications to quantum communication, quantum simulation, and quantum computing in the NISQ-era, where the choice of measurement has a direct impact on benchmarking, error-correction scheme, and protocol performance based on entanglement. The paper ends with a recommendation of contextual, purpose-based scheme of selecting entanglement measures and suggests a further study on scalable benchmarking, hybrid quantifiers, and operational performance-based entanglement measurements. These observations reinforce the theoretical premise of entanglement studies and enable the advancement of more effective quantum technologies in the field of practice.
Greenberger-Horne-Zeilinger (GHZ) states are a widely used benchmark for studying multipartite entanglement and coherence in quantum processors. In this work, GHZ states of increasing size were prepared on the 156-qubit IBM Quantum processor ibm_marrakesh and certified using a fidelity-based entanglement witness. State coherence was extracted from parity-oscillation measurements using the multiple-quantum-coherence method. The study investigates how a combination of practical error-reduction techniques affects the largest GHZ state that can be certified on open-access superconducting hardware. These techniques include depth-minimized entangling trees, calibration-aware qubit selection, dynamical decoupling with gate and measurement twirling, and matrix-free readout-error mitigation. A naive implementation fails at larger system sizes, while depth-optimized preparation certifies entanglement up to 14 qubits. Calibration-aware qubit selection extends this to 16 qubits, and readout-error mitigation enables certification of genuine multipartite entanglement up to 18 qubits with a measured fidelity exceeding the witness threshold. The results show that the achievable certification size is determined primarily by the quality of the selected qubit region rather than by the total number of qubits available on the processor. The observed non-monotonic dependence of fidelity on system size reflects variations in local device performance. These findings illustrate the impact of hardware-aware compilation and error-mitigation strategies on entanglement certification using publicly accessible quantum computing platforms.
"Quantum information" refers to the information-theoretic properties of quantum systems. There is still a general prejudice among physicists against the idea that these systems express information due to the nonlocal behavior of entangled quantum systems. The present paper calculates the information content of simple two-state entangled systems (anti-aligned spin-1/2 electron-positron pair, anti-polarized spin-1 photon pair). This calculation involves a modified application of the entropy formalism of quantum statistical mechanics. In addition, the classical and quantum analogues of mutual information are calculated for the entangled particles and experimental devices used to measure them. It is shown that the amount of information expressed by the spin measurement devices depends upon their parameter settings; the spin information of an entangled system prior to measurement is a constant. These results indicate a distinction between information available to a system's sub-components versus that available to measurement devices outside the system. This "inaccessible" information is likely carried by other physical properties of the system.