Abstract A squeezed generalized amplitude damping (SGAD) channel is a quantum channel that models a general noise process incorporating the effects of bath squeezing, dissipation, and decoherence. In this paper, we analyze the dynamics of quantum entanglement and discord in the SGAD channel with memory. By obtaining a stochastic map defining this noisy quantum channel, we derive the concurrence and discord of Werner-like mixed states sent by successive uses of the channel. It is shown that these quantum correlations can be preserved or even generated depending on the initial channel input states, channel parameters, and the degree of channel memory. In particular, the squeezing effect does not contribute to the dynamics of quantum correlation for singlet-like states under correlated noise.

I will investigate the capacities of noisy quantum channels through a combined analytical and numerical approach. First, I introduce novel flagged extension techniques that embed a channel into a higher-dimensional space, enabling single-letter upper bounds on quantum and private capacities. My results refine previous bounds and clarify noise thresholds beyond which quantum transmission vanishes. Second, I present a simulation framework that uses coherent information to estimate channel capacities in practice, focusing on two canonical examples: the amplitude damping channel (which we confirm is degradable and thus single-letter) and the depolarizing channel (whose capacity requires multi-letter superadditivity). By parameterizing input qubit states on the Bloch sphere, I numerically pinpoint the maximum coherent information for each channel and validate the flagged extension bounds. Notably, I capture the abrupt transition to zero capacity at high noise and observe superadditivity for moderate noise levels.

Quantum key distribution (QKD) offers information-theoretic security grounded in the laws of quantum mechanics, with the BB84 protocol serving as the canonical reference due to its operational simplicity and provable security. However, practical deployments face two concurrent — threats channel decoherence and active eavesdropping whose combined impact on protocol viability has been characterized only in isolation by prior literature. This paper presents a joint circuitlevel analysis of BB84 under composite channel noise and partial intercept-resend attacks, implemented on the Qiskit Aer simulator across five qubit configurations (9, 12, 16, 20, and 50 qubits) with 1024 measurement shots per experiment. A composite noise model combining depolarizing noise, amplitude damping, and readout errors is coupled with a probabilistic eavesdropper whose interception fraction ($\alpha$) is systematically varied. We derive a closed-form joint QBER expression, whose non-additive coupling term quantifies how channel corruption partially masks eavesdropping signatures, and we analytically recover the 11% security threshold from the Devetak–Winter bound. Parameter sweeps across noise strength and interception fraction reveal that even modest eavesdropping under realistic noise breaches the threshold. At $\alpha=0. 2 5$ and $50$ qubits, the observed QBER reaches 19.05%, producing a negative secure key rate and Cascade reconciliation failure. These findings establish concrete design constraint

Single-qubit channels are studied under two broad classes: amplitude damping channels and generalized depolarizing channels. A canonical derivation of the Kraus representation of the former, via the Choi isomorphism is presented for the general case of a system's interaction with a squeezed thermal bath. This isomorphism is also used to characterize the difference in the geometry and rank of these channel classes. Under the isomorphism, the degree of decoherence is quantified according to the mixedness or separability of the Choi matrix. Whereas the latter channels form a 3-simplex, the former channels do not form a convex set as seen from an ab initio perspective. Further, where the rank of generalized depolarizing channels can be any positive integer upto 4, that of amplitude damping ones is either 2 or 4. Various channel performance parameters are used to bring out the different influences of temperature and squeezing in dissipative channels. In particular, a noise range is identified where the distinguishability of states improves inspite of increasing decoherence due to environmental squeezing.

and decoherence can occur, density matrices are frequently used. Noise is often modelled via a depolarizing channel or an amplitude damping channel. In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed ensembles of states. These arise in quantum mechanics in two different situati w… Statistical mechanics uses density matrices, most prominently to express the idea that a system is prepared at a nonzero temperature. Constructing a density matrix using a canonical ensemble gives a result of the form ρ = exp ⁡ ( − β H ) / Z ( β ) {\displaystyle \rho =\exp(-\beta H)/Z(\beta )} , where β {\displaystyle \beta } is the inverse temperature ( k B T ) − 1 {\displaystyle (k_{\rm {B}}T)^{-1}} and H {\displaystyle H} is the system's Hamiltonian. The normalization condition that the trace of ρ {\displaystyle \rho } be equal to 1 defines the partition function to be Z ( β ) = t r exp ⁡ ( − β H ) {\displaystyle Z(\beta )=\mathrm {tr} \exp(-\beta H)} . If the number of particles involved in the system is itself not certain, then a grand canonical ensemble can be applied, where the states summed over to make the density matrix are drawn from a Fock space. Quantum decoherence theory typically involves non-isolated quantum systems developing entanglement with other systems, including measurement apparatuses. Density matrices make it much easier to describe the process and calculate its consequences. Quantum decoherence explains why a system interacting with an environment transitions from being a pure state, exhibiting superpositions, to a mixed state, an incoherent combination of classical alternatives. This transition is fundamentally reversible, as the combined state of system and environment is still pure, but for all practical purposes irreversible, as the environment is a very large…

Multipartite quantum steering, a unique resource for asymmetric quantum network information tasks, is very fragile to the inevitable decoherence, which makes it useless for practical purposes. It is thus of importance to understand how it decays in the presence of noise channels. We study the dynamic behaviors of genuine tripartite steering, reduced bipartite steering, and collective steering of a generalized three-qubit W state when only one qubit interacts independently with the amplitude damping channel (ADC), phase damping channel (PDC) or depolarizing channel (DC). Our results provide the region of decoherence strength and state parameters that each type of steering can survive. The results show that these steering correlations decay the slowest in PDC and some non-maximally entangled states more robust than the maximally entangled ones. Unlike entanglement and Bell nonlocality, the thresholds of decoherence strength that reduced bipartite steering and collective steering can survive depend on the steering direction. In addition, we find that not only one party can be steered by a group system, but also two parties can be steered by a single system. There is a trade-off between the monogamy relation involving one steered party and two steered parties. Our work provides comprehensive information about the effect of decoherence on multipartite quantum steering, which will help to realize quantum information processing tasks in the presence of noise environments.