The dynamics of single-qubit coherence and two-qubit entanglement are investigated in the Bloch channels with the indefinite causal order, which is created by means of a quantum switch. Coherence and entanglement are quantified respectively in terms of l 1 -norm and negativity. It is shown that both coherence and entanglement with the indefinite causal order are larger than those without the indefinite causal order. In fact, the coherence remains finite even in the long-time limit. Contrary to expectations, it becomes larger as the environmental temperature increases. Furthermore, it is found that the entanglement becomes larger and survives longer than that in the absence of the indefinite causal order.
The dynamics of single-qubit coherence and two-qubit entanglement are investigated in the Bloch channels with the indefinite causal order, which is created by means of a quantum switch. Coherence and entanglement are quantified respectively in terms of l 1 -norm and negativity. It is shown that both coherence and entanglement with the indefinite causal order are larger than those without the indefinite causal order. In fact, the coherence remains finite even in the long-time limit. Contrary to expectations, it becomes larger as the environmental temperature increases. Furthermore, it is found that the entanglement becomes larger and survives longer than that in the absence of the indefinite causal order.
We examine the emergence of dynamical memory effects in quantum processes having indefinite time direction and causal order. In particular, we focus on the class of phase-covariant qubit channels, which encompasses some of the most significant paradigmatic open quantum system models. In order to assess the memory in the time evolution of the system, we utilize the trace distance and the entanglement based measures of non-Markovianity. While the indefinite time direction is obtained through the quantum time flip operation that realizes a coherent superposition of forward and backward processes, the indefinite causal order is achieved via the quantum switch map, which implements two quantum processes in a coherent superposition of their two possible orders. Considering various different families of phase-covariant qubit channels, we demonstrate that, when implemented on memoryless quantum processes, both the quantum time flip and the quantum switch operations can generate memory effects in the dynamics according to the trace distance based measure under certain conditions. On the other hand, with respect to the entanglement based measure, we show that neither the quantum time flip nor the quantum switch could induce dynamical memory for any of the considered phase-covariant channels.
Quantum compositions of channels can grant advantages over classical compositions in quantum information processing or thermodynamical tasks. One of such quantum composition is one with indefinite causal order, where multiple quantum channels are placed in a superposition of different causal or operation orders. The advantages of indefinite causal order were demonstrated in an experimentally realizable setup known as the quantum switch and were often attributed to this new quantum resource of indefinite causality, but some doubts and disagreements still remains as compositions without indefinite causal order can achieve the same advantages. In this work, we proposed that the quantum switch's uniqueness lies in its ability to exhibit coherent non-Markovianity, where memory effects acts across different paths of superposition. We showed that the quantum switch violates completely positive or CP-divisibility and thus has intrinsic non-Markovianity in its evolution, which allows for non-Markovian backflow of information from the environment. This backflow of information can then play a role in the many advantages seen in the quantum switch, and by extending the quantum switch operation such that the non-Markovianity is controllable, we showed that these advantages depend on the presence and amount of non-Markovianity, achieving the quantum switch case when the system is fully non-Markovian. Particularly, we demonstrated this for the quantum switch's advantages in communication capacities, work extraction via daemonic ergotropy, and refrigeration via heat extraction. Other quantum compositions that are often compared to indefinite causal order, such as the superposition of independent channels and superposition of trajectories, are also captured by this extended construction of the quantum switch, and we showed that their difference with the quantum switch lies in the presence or absence of non-Markovianity. Our work suggests that non-Markovianity is an important recipe for the quantum switch or indefinite causal order, and is a nonnegligible factor for its advantages.
Indefinite causal order extends quantum information processing beyond fixed causal structures, with the quantum SWITCH serving as its canonical realization. By coherently superposing different orders of quantum channels, the quantum SWITCH has been shown to provide operational advantages in communication, computation, metrology, and related tasks. Despite these advances, the physical resources responsible for these advantages remains unclear. Recent studies have further revealed that the quantum SWITCH can generate memory effects, manifested as non-Markovian information backflow. In this work, we examine the origin of such memory and determine whether they reflect genuine (quantum) non-Markovianity or instead arises from classical origin. To this end, we analyze two representative scenarios: one based on discrete-time evolution and another formulated through dynamical maps in open quantum systems. We show that the memory effects generated by the quantum SWITCH are not genuinely quantum non-Markovian, thereby prompting a re-examination of the source of quantum advantage in indefinite causal order frameworks.
Abstract In this proceeding, we revisit the discussion presented in Ref. [Commun Phys 7, 373 (2024)], which examines the behavior of a quantum switch involving two arbitrary quantum operations when the control is exposed to environmental effects. Our study extends this analysis by focusing on the evolution of entanglement in the target system within the quantum switch framework, taking into account the influence of environmental conditions and control post-selection. We find that entanglement evolution is highly sensitive to these factors. While entanglement sudden death occurs under definite causal order, indefinite causal order can reverse this loss. We observe entanglement revival in high-temperature regimes and a sudden reappearance of entanglement under weak monitoring conditions at low temperatures. These findings provide insights into the resilience of the quantum switch in the presence of environmental disturbances and highlight its potential for applications where preserving entanglement is essential.
The combined use of quantum channels can grant communication advantages in the form of enhancements to communication capacities. One such channel composition is the quantum switch, which implements a system with indefinite causal order by coherent control of the orderings of two or more quantum channels, resulting in enhanced communication capacities. Here, using the monogamy relation, we studied the flow of entanglement monotone in these quantum compositions of channels in the environmental representation. We implemented the two-party quantum switch in this framework, and demonstrated that non-Markovianity is the source of revival of the entanglement monotone in this setup. The possibility and amount of revival was shown to depend on the entangling capability of the channels, and the perfect activation of coherent information with entanglement-breaking channels was also replicated with the perfect revival of entanglement monotone. Additionally, we showed that a more general non-Markovian circuit can still grant enhancements to coherent information and Holevo quantity without the presence of indefinite causal order.
Indefinite causal order (ICO), in which the order of quantum operations is placed in a coherent superposition, has been demonstrated to enhance various information-processing tasks. Here, we investigate its impact on the thermodynamic processes generated by thermalizing quantum channels. We consider a two-level system interacting with two thermal baths under a quantum SWITCH, with the channel order controlled coherently by an ancillary qubit. We derive closed-form expressions for the effective inverse temperature βf of the postselected system state for both identical and distinct bath temperatures, and identify the control-qubit parameters that maximize heating or cooling. Our analysis reveals how the diagonal and coherent components of the control-qubit state contribute separately to the temperature shift, and how their interplay enables departures from the thermal response attainable under protocols with a definite causal order within the thermodynamic setting considered here. Bath asymmetry enhances these effects, while reduced purity of the control qubit state suppresses them. These results provide a systematic framework for assessing SWITCH-based thermalization in the setting of indefinite causal order, and identify control-qubit coherence as a tunable resource.