From the point of view of communication theory, a quantum channel can be defined as a physical process mapping from initial to final state in the form of CPTP (Completely positive trace preserving) map. Quantum information theory provide a theoretical framework and some mathematical methods to accomplish this. In order to preserve information, we proposed a scheme for the protection of two-qubit state through various noise channel, where successive uses of noise channels are correlated. These successive uses of channels are called memory. Different types of noise channels with memory have been discussed in details. We compare the dynamics of entanglement of two-qubit state under different noise channel and it has been seen that one can preserve two-qubit steady state quantum correlation under noise channels with memory. The study of memory effect in quantum channel will emerge as an interesting phenomena to trace back information from the surrounding which is considered as a resource in quantum information task. However, we also define some mores measures of entanglement and their preservation. We hope that our new findings may help to study the two-qubit entanglement structure.
Quantum temporal correlations exhibited by violations of Leggett-Garg Inequality (LGI) and Temporal Steering Inequality (TSI) are in general found to be non-increasing under decoherence channels when probed on two-qubit pure entangled states. We study the action of decoherence channels, such as amplitude damping, phase-damping and depolarising channels when partial memory is introduced in a way such that two consecutive uses of the channels are time-correlated. We show that temporal correlations demonstrated by violations of the above temporal inequalities can be protected against decoherence using the effect of memory.
Quantum anomalies strongly constrain the possible behavior of many-body systems. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which relates UV symmetry and filling constraints to IR features of the energy spectrum and ground-state structure. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the Liouvillian of a
d-dimensional repeated quantum channel with a mixed anomaly between strong
S and weak
G symmetry can be mapped to a
(d+1)-dimensional mixed-state symmetry-protected topological (mSPT) phase. Under this correspondence, the initial and steady states of the channel are identified with boundary states of the higher-dimensional mSPT in the presence of bulk projection. We further introduce the twisted Renyi-
N correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Finally, we identify the \textit{Liouvillian singular spectrum}, rather than the Liouvillian spectrum itself, as a more fundamental diagnostic of quantum anomalies, and show that it is dual to the operator entanglement spectrum of the mSPT.