# Publications

**Authors: **Timothée Hoffreumon and Ognyan Oreshkov

**Year:** 2021

We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined causal order of events locally. We characterise the higher-order process describing such correlations, which we name the multi-round process matrix (MPM), and formulate a notion of causal nonseparability for it that extends the one for standard PMs. We show that in the multi-round case there are novel manifestations of causal nonseparability that are not captured by a naive application of the standard PM formalism: we exhibit an instance of an operator that is both a valid PM and a valid MPM, but is causally separable in the first case and can violate causal inequalities in the second case due to the possibility of using a side channel.

**Authors: **Lin-Qing Chen

**Year:** 2021

Through the analysis of null symplectic structure, we derive the condition for integrable Virasoro generators on the covariant phase space of axisymmetric Killing horizons. A weak boundary condition selects a special relationship between the two temperatures for the putative CFT. When the integrability is satisfied for both future and past horizons, the two central charges are equal. At the end we discuss the physical implications.

**Authors: **Esteban Castro-Ruiz, Ognyan Oreshkov

**Year:** 2021

Recently, there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles and physical meaning is still lacking. Here, we develop a framework for quantum reference frame transformations that focuses on the algebra of relative observables between a system and a reference frame. We show that this perspective sheds light on important conceptual issues regarding reference frame changes. In our framework, a quantum reference frame viewpoint is a preferred partition of the full invariant system into subsystems. A transformation between quantum reference frames is a specific change of preferred partition. Interestingly, the full invariant system contains not only the algebra of relative observables between the system and frame but also an “extra particle,” related to the invariant degrees of freedom of the frame itself. The extra particle contains information about the “quantumness” of the frame and is essential to the unitarity of the transformations. Our approach can be applied to a vast set of symmetry groups and systems, among which we study the centrally extended Galilei group as a particular case.

**Authors: **Julian Wechs, Cyril Branciard, Ognyan Oreshkov

**Year:** 2022

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 such processes can be realised in practice. In order to provide a rigorous argument for the notion that certain such processes have a realisation in standard quantum theory, the concept of time-delocalised quantum subsystem has been introduced. In this paper, we show that realisations on time-delocalised subsystems exist for all unitary extensions of tripartite processes. Remarkably, this class contains processes that violate causal inequalities, i.e., that can generate correlations that witness the incompatibility with definite causal order in a device-independent manner. We consider a known striking example of such a tripartite classical process that has a unitary extension, and study its realisation on time-delocalised subsystems. We then discuss the question of what a violation of causal inequalities implies in this setting, and argue that it is indeed a meaningful concept to show the absence of a definite causal order between the variables of interest.

**Authors: ** Ravi Kunjwal, Ämin Baumeler

**Year:** 2022

We show a correspondence between quantum nonlocality without entanglement and logically consistent classical processes without causal order. Three parties with access to a noncausal classical process — the AF/BW process — can perfectly discriminate the states in an ensemble — the SHIFT ensemble — exhibiting quantum nonlocality without entanglement, something impossible with local operations and classical communication (LOCC): The LOCC restriction implicitly assumes causal classical communication. This provides an operational interpretation of the AF/BW process as a noncausal information-theoretic resource. From a foundational perspective, this means that the ability to perfectly discriminate quantum states in the SHIFT ensemble via local operations and classical communication would serve as an operational witness of noncausality. We then generalize our result to show how any Boolean classical process without global past can be transformed to an ensemble of states that exhibits quantum nonlocality without entanglement. Since multipartite generalizations of the AF/BW process are known, this yields novel multiqubit ensembles of quantum nonlocality without entanglement, which is of independent interest.