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It has been shown that it is theoretically possible for there to exist quantum and classical processes in which the operations performed by separate parties do not occur in a well-defined causal order. A central question is whether and how…

One can theoretically conceive of processes where the causal order between quantum operations is no longer well-defined. Certain such causally indefinite processes have an operational interpretation in terms of quantum operations on…

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal…

The recent years have seen interest into the possibility for (classical as well as quantum) causal structures that, while remaining logically consistent, feature a cyclic causal order between events, opening intriguing possibilities for new…

Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by sets of parties operating in a definite causal order. Since the…

The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders.…

In recent years many works have explored possible advantages of indefinite causal order, with the main focus on its controlled implementation known as quantum switch. In this paper, we tackle advantages in quantum thermodynamics, studying…

A quantum-controlled device may produce a scenario in which two general quantum operations can be performed in such a way that it is not possible to associate a definite order for the operations application. Such an 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…

A switched quantum channel with indefinite causal order is studied for the fundamental metrological task of phase estimation on a qubit unitary operator affected by quantum thermal noise. Specific capabilities are reported in the switched…

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.…

Quantum processes with indefinite causal order -- so-called causally nonseparable processes -- can exhibit various advantages over quantum circuits with a fixed or a well-defined causal structure. A natural question is how much…

This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e.,…

Quantum theory departs from classical physics in its treatment of correlations, most prominently through the phenomena of contextuality and nonlocality. Once regarded primarily as foundational curiosities, these effects are now understood…

A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is…

The release of causal structure of physical events from a well-defined order to an indefinite one stimulates remarkable enhancements in various quantum information tasks. Some of these advantages, however, are questioned for the ambiguous…

Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…

A quantum switch is a superoperator that, in general, creates a superposition of various causal orders of two or more quantum dynamics that are all divisible in the complete positivity (CP) sense. We introduce a process that we term as the…

Bell inequalities follow from a set of seemingly natural assumptions about how to provide a causal model of a Bell experiment. In the face of their violation, two types of causal models that modify some of these assumptions have been…

Since Bell's theorem, it is known that the concept of local realism fails to explain quantum phenomena. Indeed, the violation of a Bell inequality has become a synonym of the incompatibility of quantum theory with our classical notion of…