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arXiv:2204.08149 · Annalen der Physik

Phase Covariant Channel: Quantum Speed Limit of Evolution

Riya Baruah, K. G. Paulson, Subhashish Banerjee

Published Nov 21, 2022• 8 citations
arXivHTMLPDF

Abstract

Abstract The quantum speed of evolution for the phase covariant map is investigated. This involves absorption, emission, and dephasing processes. The maps under various combinations of the above processes are considered to investigate the effect of phase covariant maps on quantum speed limit time. For absorption‐free phase covariant maps, combinations of dissipative and CP‐(in)divisible (non)‐Markovian dephasing noises are considered. The role of coherence‐mixedness balance on the speed limit time is checked in the presence of both vacuum and finite temperature effects. The rate at which Holevo's information changes and the action quantum speed of evolution for specific cases of the phase covariant map are also investigated.

DOI
10.1002/andp.202200199

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Abstract The quantum speed of evolution for the phase covariant map is investigated. This involves absorption, emission, and dephasing processes. The maps under various combinations of the above processes are considered to investigate the effect of phase covariant maps on quantum speed limit time. For absorption‐free phase covariant maps, combinations of dissipative and CP‐(in)divisible (non)‐Markovian dephasing noises are considered. The role of coherence‐mixedness balance on the speed limit time is checked in the presence of both vacuum and finite temperature effects. The rate at which Holevo's information changes and the action quantum speed of evolution for specific cases of the phase covariant map are also investigated.
Abstract The minimum evolution time between multi-qubit quantum states is estimated for non-Markovian quantum channels. We consider the maximally coherent pure and mixed states as well as multi-qubit X states as initial states and discuss the impact of initial coherence and the behaviour of coherence on their speed of evolution for both dephasing and dissipative processes. The role of the non-zero value of initial coherence under information backflow conditions for the non-unital dissipative process is revealed by the flow of quantum speed limit time ( τ QSL ). The trade-off between mixedness and coherence on the speed limit time reveals the nature of the quantum process the states undergo. The complementarity effect between mixedness and coherence is more prominent in the quantum non-unital dissipation process. The parametric trajectory of speed limit time vividly depicts the difference in the evolution of pure and mixed initial states, and this could be used to distinguish between the unital and non-unital channels studied in this work. Our investigation of quantum speed limit time on multi-qubit entangled X states reveals that τ QSL can be identified as a potential dynamical witness to distinguish multi-qubit states in the course of evolution.
Abstract Quantum theory sets a fundamental bound for the minimal time evolution between initial and final state of a system . This bound is called quantum speed limit time , which is used to quantify the speed of evolution of a quantum system. If quantum speed limit time decreases, the evolution keeps on increasing. In this paper, we study the effect of quantum speed limit time in terms of correlated and uncorrelated noise channels like amplitude damping and phase damping channel. We use maximally entangled mixed state as our initial state. We observe the behavior of quantum speed limit time under Markovian and non-Markovian dynamics. We prove that for the special class of our inital state and for the dynamical evolution of a system, there exist a link between quantum speed limit time and non-Markovianity. However, an interesting results were also observed regarding the tightness of bound in Markovian region. Our results shed light on the information back-flow between system and environment in terms of quantum evolution which is useful as a resource in quantum information processing task.
Quantum speed limit time defines the limit on the minimum time required for a quantum system to evolve between two states. Investigation of bounds on speed limit time of quantum system under non-unitary evolution is of fundamental interest, as it reveals interesting connections to quantum (non-)Markovianity. Here, we discuss the characteristics of quantum speed limit time as a function of quantum memory, quantified as the deviation from temporal self-similarity of quantum dynamical maps for CP-divisible as well as indivisible maps. This provides an operational meaning to CP-divisible (non-)Markovianity.
Abstract The time required for a given quantum system to evolve is known as the quantum speed limit (QSL), which can be used to characterize the speed of evolution of a quantum system. We study QSL time for Markovian and non-Markovian dynamics. Investigating the effect of QSL under non-unitary evolution is of fundamental interest. In this work, we derive QSL time for maximally entangled state and apply its results under various noise channels. We discuss measure of QSL, how correlations affect the rate of QSL. Further, we carried an investigation on connection between non-Markovianity and QSL. We show that the non Markovian evolution can speed up quantum evolution, therefore lead to smaller QSL time. We have established the connections between correlated channels, information loss and non-Markovianity. This theory may suggest some further connections to retrieve back information from surrounding and preserves decoherence.
Abstract The quantum speed limit and the Wigner function of open system models are studied. To this end, the phase covariant and a two‐qubit model interacting with a squeezed thermal bath via position‐dependent coupling are used. The dependence of the coupling on the position of the qubits allows for the study of the dynamics in the collective regime, which is conducive to speeding up the evolution. An interesting interplay is observed between non‐Markovian behavior, quantumness, and the quantum speed limit. The presence of quantum correlations is seen to speed up the evolution.
Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates γz(t)\gamma_{z}(t)γz​(t) , γ−(t)\gamma_{-}(t)γ−​(t) , and γ+(t)\gamma_{+}(t)γ+​(t) , respectively. Non-negative rates correspond to completely positive divisible dynamics, which can still exhibit such peculiarities as non-monotonicity of populations for any initial state. We find a set of quantum channels attainable in the completely positive divisible phase covariant dynamics and show that this set coincides with the set of channels attainable in semigroup phase covariant dynamics. We also construct new examples of eternally indivisible dynamics with γz(t)<0\gamma_{z}(t)<0γz​(t)<0 for all t>0t>0t>0 that is neither unital nor commutative. Using the quantum Sinkhorn theorem, we for the first time derive a restriction on the decoherence rates under which the dynamics is positive divisible, namely, γ±(t)≥0\gamma_{\pm}(t)\geq 0γ±​(t)≥0 , γ+(t)γ−(t)+2γz(t)>0\sqrt{\gamma_{+}(t)\gamma_{-}(t)}+2\gamma_{z}(t)>0γ+​(t)γ−​(t)​+2γz​(t)>0 . Finally, we consider phase covariant convolution master equations and find a class of admissible memory kernels that guarantee complete positivity of the dynamical map.