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Register a new userIndefinite Causal Orders from Superpositions in Time
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Treating the time of an event as a quantum variable, we derive a scheme in which superpositions in time are used to perform operations in an indefinite causal order. We use some aspects of a recently developed space-time-symmetric formalism of events. We propose a specific implementation of the scheme and recover the Quantum SWITCH, where quantum operations are performed in an order which is entangled with the state of a control qubit. Our scheme does not rely on any exotic quantum gravitational effect, but instead on phenomena which are naturally fuzzy in time, such as the decay of an excited atom.
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In quantum mechanics events can happen in no definite causal order: in practice this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Indefinite causal order can be observed in a quantum switch, where two operations act in a quantum superposition of the two possible orders. Here we realise a photonic quantum switch, where polarisation coherently controls the order of two operations, $hat{A}$ and $hat{B}$, on the transverse spatial mode of the photons. Our setup avoids the limitations of earlier implementations: the operations cannot be distinguished by spatial or temporal position. We show that 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.
Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a direct connection to the theory of multi-time quantum states. Specifically, we show that process matrices are equivalent to a particular class of pre- and post- selected quantum states. This offers a new conceptual point of view to the nature of process matrices. Our results also provide an explicit recipe to experimentally implement any process matrix in a probabilistic way, and allow us to generalize some of the previously known properties of process matrices. Furthermore we raise the issue of the difference between the notions of indefinite temporal order and indefinite causal order, and show that one can have indefinite causal order even with definite temporal order.
Investigating the role of causal order in quantum mechanics has recently revealed that the causal distribution of events may not be a-priori well-defined in quantum theory. While this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. Here we report the first decisive demonstration of a process with an indefinite causal order. To do this, we quantify how incompatible our set-up is with a definite causal order by measuring a causal witness. This mathematical object incorporates a series of measurements which are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment we perform a measurement in a superposition of causal orders - without destroying the coherence - to acquire information both inside and outside of a causally non-ordered process. Using this information, we experimentally determine a causal witness, demonstrating by almost seven standard deviations that the experimentally implemented process does not have a definite causal order.
Realization of indefinite causal order (ICO), a theoretical possibility that even causal relations between physical events can be subjected to quantum superposition, apart from its general significance for the fundamental physics research, would also enable quantum information processing that outperforms protocols in which the underlying causal structure is definite. In this paper, we start with a proposition that an observer in a state of quantum superposition of being at two different relative distances from the event horizon of a black hole, effectively resides in ICO space-time generated by the black hole. By invoking the fact that the near-horizon geometry of a Schwarzschild black hole is that of a Rindler space-time, we propose a way to simulate an observer in ICO space-time by a Rindler observer in a state of superposition of having two different proper accelerations. By extension, a pair of Rindler observers with entangled proper accelerations simulates a pair of entangled ICO observers. Moreover, these Rindler-systems might have a plausible experimental realization by means of optomechanical resonators.
One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix framework. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several observers, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such observers with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the physical implementation of process matrices and on the perspectives of the observers as described via causal reference frames. While it allows for describing scenarios where different definite causal orders are coherently controlled, we explain why certain non-causal processes might not be implementable within this setting.
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