Experimental investigation of the uncertainty principle in the presence of quantum memory (1012.0332v1)

Abstract: Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a particle (stored in a quantum memory) which is entangled with the system, his uncertainty is generally reduced. This effect has recently been quantified by Berta et al. [Nature Physics 6, 659 (2010)] in a new, more general uncertainty relation, formulated in terms of entropies. Using entangled photon pairs, an optical delay line serving as a quantum memory and fast, active feed-forward we experimentally probe the validity of this new relation. The behaviour we find agrees with the predictions of quantum theory and satisfies the new uncertainty relation. In particular, we find lower uncertainties about the measurement outcomes than would be possible without the entangled particle. This shows not only that the reduction in uncertainty enabled by entanglement can be significant in practice, but also demonstrates the use of the inequality to witness entanglement.

• The paper demonstrates that incorporating quantum memory significantly reduces measurement uncertainty, confirming theoretical predictions.
• Using entangled photon pairs via SPDC in a Sagnac interferometer, the authors validate Berta et al.'s revised entropic inequality.
• Findings have implications for quantum cryptography and serve as an effective entanglement witness in advanced quantum information protocols.

Experimental Investigation of the Quantum Memory-Based Uncertainty Principle

The paper provides a detailed experimental exploration of the uncertainty principle within the framework of quantum mechanics, specifically considering the role of quantum memory. The research revisits the well-established concept of Heisenberg's uncertainty principle by incorporating quantum entanglement to reduce observer uncertainty during simultaneous measurements. The original uncertainty principle provided boundaries on precision for measurements like position and momentum. The recent theoretical advancement by Berta et al. modified this principle, introducing entropy as a measure and allowing quantum memory to alter the level of uncertainty.

Theoretical Framework and Experimental Setup

Berta et al. derived a new uncertainty relation as a function of entropic measures, represented mathematically as:

$H(R|B) + H(S|B) \geq \log_{2}\frac{1}{c} + H(A|B),$

where $R$ and $S$ are the observables, and the conditional von Neumann entropy terms $H(R|B)$ and $H(S|B)$ express the uncertainty given access to a quantum memory $B$. This framework highlights how entanglement can reduce uncertainty, effectively witnessing quantum entanglement.

The authors use an experimental setup involving entangled photon pairs created through spontaneous parametric down-conversion (SPDC) within a Sagnac interferometer. One photon serves as the system under observation while the other acts as quantum memory. Measurements are staggered temporally using an optical delay line, allowing communication (feed-forward) of measurement choice between Alice, who performs the measurement, and Bob, who holds the quantum memory.

Empirical Results

Experimentation confirms that the use of quantum memory does indeed reduce uncertainty. Across various entanglement degrees and observable pair configurations, researchers found entropic uncertainties lower than classical counterparts. Particularly telling are results with maximally entangled states and complementary observables. Here, uncertainties could be eliminated entirely, $H(X|B) + H(Z|B) = 0$, showcasing perfect predictability when the system is maximally entangled.

This diminished uncertainty strongly aligns with Berta et al.’s revised uncertainty relation, emphasizing the capacity for quantum memory to significantly impact measurement outcomes. The empirical findings provide robust support for theoretical predictions, particularly in the context of interpretation and practical applications.

Implications and Future Directions

The practical implications of these results are significant. The ability to reduce measurement uncertainty has profound implications for fields such as quantum cryptography, where secure information transmission could leverage quantum memory's properties. The findings also provide a basis for using the new inequality as an effective entanglement witness — an experimental tool to discern entangled from separable states.

Looking forward, enhancements in photonic sources and detection technologies could push the boundaries of this research, enabling higher precision in testing such quantum mechanical principles. Furthermore, this foundational work sets the stage for exploring other quantum information protocols that harness the potential of entropic uncertainty within quantum systems. The broader reach of such studies could contribute to innovations in quantum computing and secure quantum communication networks.

In conclusion, this research elegantly reinforces the modified uncertainty principle proposed by Berta et al., with robust experimental evidence highlighting the tangible benefits of entanglement and quantum memory in reducing uncertainty. As technology progresses, expanding the exploration of quantum mechanics through these innovative experimental methodologies will undoubtedly catalyze advancements across quantum sciences and technologies.