We show that quantum indefinite causal structure generically reduce two-party correlations. For significant indefiniteness in the causal structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers an operational model-independent ultraviolet regularization mechanism. It may be applied to various approaches of quantum gravity that allow quantum indefinite spacetime causal structure.
We show that quantum indefinite causal structure generically reduce two-party correlations. For significant indefiniteness in the causal structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers an operational model-independent ultraviolet regularization mechanism. It may be applied to various approaches of quantum gravity that allow quantum indefinite spacetime causal structure.
We adopt an operational mode of thinking to study spacetime fluctuations and their impacts on questions of quantum gravity. Particular emphasis is put on studying causal structure fluctuations. The study is guided by the principle of causal neutrality, which says that fundamental concepts and laws of physics should be stated without assuming a definite spacetime causal structure. Most traditional concepts and theories of physics violate this principle. A major theme of this thesis is to upgrade the traditional concepts and theories in accordance with the principle of causal neutrality. \n \nAmong other things, the thesis include works on the following. (1) An axiomatic derivation of the complex Hilbert space structure of quantum theory without assuming definite causal structure. (2) A so-called causally neutral quantum field theory (CNQFT) framework for algebraic quantum physics allowing indefinite causal structure. (3) A proposal that causal fluctuation regularizes quantum field ultraviolet divergences (UV) and that the UV regularizing correlation functions with causal fluctuations characterize the UV structure of physical states. (4) A study on quantitative measures of causality. (5) A so-called ``correlation networks'' framework to study quantum theory with indefinite causal structure, which generalizes previous frameworks. (6) New definitions of entanglement and entanglement measures that conform to the causal neutrality principle. (7) Ideas on finding a causally neutral analogue of Einstein's equation for quantum spacetime. (8) A simple theorem showing that the communication capacities of general correlations (with definite or indefinite causal structure) defined with respect to state transmission can be reduced to those of channels.
The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being causally connected and not, can they still be entangled? If so, how does one measure the amount of entanglement? We propose to generalize the notions of entanglement and entanglement measure to address these questions. Importantly, the generalization opens the path to study quantum entanglement of states, channels, networks, and processes with definite or indefinite causal structure in a unified fashion, e.g., we show that the entanglement distillation capacity of a state, the quantum communication capacity of a channel, and the entanglement generation capacity of a network or a process are different manifestations of one and the same entanglement measure.
Quantum causality extends the conventional notion of the fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational—e.g., towards a theory of quantum gravity—to the applied—e.g., for advantages in communication and computation. In this review, the authors will walk through the basic theory of indefinite causal order and focus on experiments that rely on a physically realizable indefinite causal ordered process—the quantum switch.
One of the key ways in which quantum mechanics differs from relativity is that it requires a fixed background reference frame for spacetime. In fact, this appears to be one of the main conceptual obstacles to uniting the two theories. Additionally, a combination of the two theories is expected to yield non-classical, or "indefinite", causal structures. In this paper, we present a background-independent formulation of the process matrix formalism – a form of quantum mechanics that allows for indefinite causal structure – while retaining operationally well-defined measurement statistics. We do this by postulating an arbitrary probability distribution of measurement outcomes across discrete "chunks" of spacetime, which we think of as physical laboratories, and then requiring that this distribution be invariant under any permutation of laboratories. We find (a) that one still obtains nontrivial, indefinite causal structures with background independence, (b) that we lose the idea of local operations in distinct laboratories, but can recover it by encoding a reference frame into the physical states of our system, and (c) that permutation invariance imposes surprising symmetry constraints that, although formally similar to a superselection rule, cannot be interpreted as such.
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach time and causality. For instance, causal structure in relativity is determined by the distribution of mass in spacetime while, in the quantum formalism, it is supposed to be fixed and given in advance. In this master's thesis, we discuss the notion of indefinite order, which first appears in an abstract generalization of Quantum Theory [...] where the demand for global causal structure is removed, in principle allowing cases for which the order of operations in protocols is not necessarily well defined. One epitomical example of indefinite order is the quantum switch process, which realizes a quantum superposition of orders of two operations on a target system. The quantum switch probabilities have been reproduced in experimental optical setups that are fully described in principle by quantum mechanics. Since these experiments are compatible with spacetime causal structure, this generated uncertainty about the conclusions that can be drawn from obtaining these results depending on the context. Here, we return to the initial motivations and also present how scenarios involving gravity in low energies could lead to indefinite order. This includes the formulation of a quantum switch in a quantum gravity scenario and of a quantum switch in a classical Schwarzschild metric. The switch then provides a common ground to discuss different kinds of setups. The latter proposal of a quantum switch in a classical metric is an original work that, aside from being an example of indefinite order, proposes the realization of the protocol in Earth's gravity as a test of quantum mechanics on curved spacetimes, a regime which has not yet been explored experimentally.
Introduction Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a formalism-local (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time-evolving state picture, the histories approach, and the local-equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how quantum theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of quantum theory. This formulation, however, may be particularly relevant to the problem of finding a theory of quantum gravity. The problem of quantum gravity is to find a theory that reduces in appropriate limits to general relativity and quantum theory (including, at least, those situations in which those two theories have been experimentally confirmed).