Experimental Verification of an Indefinite Causal Order (1608.01683v2)

Abstract: 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.

• The paper introduces an experimental quantum SWITCH setup that generates indefinite causal order, challenging classical causal sequences.
• The experiment employs a causal witness to objectively measure causal non-separability, with results deviating by seven standard deviations.
• These findings imply potential advancements in quantum computing and secure communication by leveraging quantum superpositions.

Experimental Verification of an Indefinite Causal Order

The paper entitled "Experimental Verification of an Indefinite Causal Order" presents a significant advancement in quantum mechanics, specifically concerning the concept of indefinite causal order. The work articulates an experimental setup that demonstrates a process where the causal order of events is not definite—a concept traditionally considered paradoxical within the classical understanding of physical phenomena.

Theoretical Foundations

Quantum mechanics introduces the possibility of non-classical causal structures due to the superposition principle. The paper explores how applying superposition to causal orders can result in scenarios without a well-defined sequence of events. This challenges the conventional view that one event must causally lead to another in a linear, time-ordered manner. Instead, the concept of a 'quantum SWITCH' is introduced as a mechanism to achieve this indefinite causal order by superimposing the order of unitary operations on quantum states.

Experimental Setup and Methodology

The core of the experiment involves using a quantum SWITCH to create a superposition of two causal orders. The setup encodes the control qubit in the path degree of freedom of a photon and the target qubit in the photon's polarization. Alice and Bob perform operations on these qubits in superpositions of sequences, thus achieving a process where the order is indefinite. Key to this experimentation is the development of a 'causal witness,' a theoretical construct designed to assess causal indefiniteness objectively.

Causal Witness and Non-Separability

A causal witness is a mathematical tool analogous to an entanglement witness in quantum information theory. It is used to measure the degree to which a process is causally non-separable. The paper intricately details how the experimental setup measures this causal witness, demonstrating a result that deviates by seven standard deviations from the hypothesis of a definite causal order.

Results and Analysis

The experiment unequivocally confirms an indefinite causal order by leveraging an optimal causal witness that distinguishes between causally separable and non-separable processes. The findings indicate that under controlled laboratory conditions, quantum mechanics permits a coherent superposition of different causal orders. This result shows a causal non-separability that withstands certain levels of noise, highlighting the robustness of the quantum SWITCH.

Implications and Future Perspectives

This experimental demonstration has profound implications for quantum information processing, where indefinite causal orders could provide enhanced computational efficiencies and more secure communication protocols. The paper speculates on future applications, suggesting that this paradigm could yield practical advantages in quantum computing tasks that are constrained by classical causality.

Moreover, the implementation of a measurement inside the quantum SWITCH without losing coherence marks a technological stride toward realizing complex quantum processes that exploit these indefinite orders. This approach could inform future experimental designs aiming at further exploiting quantum superpositions of processes.

Conclusion

The experimental verification of indefinite causal order invites reconsideration of fundamental concepts in physics, primarily causality. The use of quantum SWITCHes and the measurement of causal witnesses present a methodical approach to probing the boundaries of causal structures in quantum mechanics. While the current work lays a robust experimental foundation, the exploration of indefinite causal orders is anticipated to expand, further uncovering the nuances of quantum causality and broadening the horizon for technologically exploiting quantum properties.