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.
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 superposition of causal orders shows promise in various quantum technologies. However, the fragility of quantum systems arising from environmental interactions, leading to dissipative behavior and irreversibility, demands a deeper understanding of the possible instabilities in the coherent control of causal orders. In this work, we employ a collisional model to investigate the impact of an open control system on the generation of interference between two causal orders. We present the environmental instabilities for the switch of two arbitrary quantum operations and examine the influence of environmental temperature on each potential outcome of control post-selection. Additionally, we explore how environmental instabilities affect protocol performance, including switching between mutually unbiased measurement observables and refrigeration powered by causal order superposition, providing insights into broader implications. Using the quantum switch—a process involving a controlled operation followed by post-selection of the control—a system of interest can evolve under an effective dynamics governed by a superposition of operation orders. This work investigates how environmental influences on the control impact the desired superposition of orders in realistic scenarios.
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.
The release of the causal structure of physical events from a well-defined order to an indefinite order stimulates remarkable enhancements in various quantum information tasks. Some of these advantages, however, are questioned for the ambiguous role of the control system in the quantum switch, which is an experimentally realized process with an indefinite causal structure. In communications, for example, not only the superposition of alternative causal orders, but also the superposition of alternative trajectories can accelerate information transmissions. Here, we follow the proposal of Liu et al. [Phys. Rev. Lett. 129, 230604 (2022)], and examine the information enhancement effect of indefinite causal orders with the toolkit of thermodynamics in a photonic platform. Specifically, we simulate the thermal interaction between a system qubit and two heat baths embedded in a quantum switch by implementing the corresponding switched thermal channels. Although its action on the system qubit only is thermally free, our results suggest that the quantum switch should be seen as a resource when the control qubit is also considered. Moreover, we characterize the non-Markovian property in this scenario by measuring the information backflows from the heat baths to the system qubit.
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.
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.
Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operations A[over ^] and B[over ^] act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound.