Asymmetry Boosts Quantum Walker Delocalization and Position

Researchers are increasingly focused on harnessing the principles of quantum walks for advanced computation and simulation. Hao Zhao, Qiyan He, and Fengzhi Yang, from the College of Physics and Electronic Science at Hubei Normal University, alongside colleagues including Cui Kong, Huiyun Cao, Tianqi Yan, Bingrui Zhong, Kaikun Tian, Jiguo Wang, Chuanjia Shan, and Jibing Liu, detail a novel investigation into asymmetric discrete-time quantum walks. Their work, conducted entirely within the College of Physics and Electronic Science, Hubei Normal University, demonstrates a method for enhancing both delocalization and entanglement through the manipulation of asymmetry factors within these walks. This research is significant because it provides a pathway towards more robust and efficient photonic quantum systems, potentially improving the performance of quantum technologies and offering an ideal platform for investigating fundamental aspects of quantum behaviour.

For years, controlling the spread of quantum particles has presented a considerable challenge to physicists. Now, a new experiment utilising photonic walks demonstrates a method for simultaneously improving both how widely a particle spreads and its ability to exist in multiple places at once. This approach uses asymmetry to achieve enhanced delocalization, even when faced with signal loss.

Scientists are increasingly focused on harnessing the principles of quantum mechanics to develop technologies beyond the capabilities of classical physics. Among the most promising areas of investigation are quantum walks, the quantum analogue of classical random walks, which exhibit ballistic spreading due to quantum interference rather than the Gaussian diffusion seen in their classical counterparts.

This unique property allows quantum walks to achieve exponential speedup in certain computational tasks, making them attractive for applications in quantum search algorithms, computing, and simulation. Recent work has concentrated on discrete-time quantum walks (DTQWs), where the walker’s movement is dictated by a ‘coin’ operation, and these systems offer a powerful means of studying non-Hermitian phenomena and generating hybrid entanglement.

Yet, maintaining and enhancing both delocalization and entanglement remains a significant challenge, particularly in the presence of environmental disturbances. Specifically, asymmetric polarization-dependent losses can disrupt the delicate quantum state, reducing the probability of finding the walker in certain locations and hindering its potential for information processing.

Researchers have demonstrated a method for simultaneously improving delocalization and entanglement in asymmetric DTQWs, while also increasing their resistance to these asymmetric losses. This was achieved through careful manipulation of coin parameters and initial states within a specifically designed experimental setup. At the heart of this advance lies a 16-step asymmetric DTQW implemented using a time-multiplexing fibre loop structure.

Unlike previous optical implementations that rely on bulky spatial displacement schemes, this time-multiplexed approach encodes photon position within the time domain, allowing for longer walk steps and precise control over the walker’s internal states. By varying asymmetric coin operations, asymmetric initial states, and asymmetric polarization-dependent losses, the team numerically calculated the inverse participation ratio and entanglement entropy of the walker.

These calculations revealed that specific coin parameters, when combined with an asymmetric initial state, could simultaneously enhance both coin-position entanglement and delocalization. Observations show that with finite asymmetric polarization-dependent loss, the probability of finding a photon on the left side of the walk decreases, while the probability on the right side increases and becomes more localized.

However, under specific coin parameters, both entanglement and delocalization exhibited improved robustness against these losses, suggesting a pathway towards more stable and reliable quantum systems. These results confirm that DTQWs represent an ideal platform for investigating photonic delocalization and hybrid entanglement, opening new avenues for strong quantum-state preparation and potentially impacting future quantum technologies.

Time-multiplexed fibre loop realises extended quantum walks with controlled polarisation

A 16-step discrete-time quantum walk (DTQW) underpinned this work, constructed using a time-multiplexing fibre loop structure. This configuration encodes different photon position states within the time domain, allowing for a greater number of walk steps than traditional spatial displacement schemes. The fibre loop provides precise control over the walker’s internal states and expands the accessible position space, overcoming limitations in scalability and stability associated with bulk optical setups.

Establishing the quantum walk’s behaviour necessitated careful consideration of initial conditions. The initial state of the quantum walker was expressed as a superposition, [cos φ |H⟩+ i sin φ |V ⟩] |0⟩, where φ defines a parameter controlling the initial polarisation. By varying this parameter alongside coin and loss parameters, researchers aimed to explore the interaction between delocalization and coin-position entanglement.

The core of the DTQW relies on alternating coin and shift operations. The coin operator, defined as a matrix acting on the photon’s polarisation, introduces the asymmetry central to the study. Following each coin operation, a conditional shift operator moves the photon left or right depending on its polarisation state. This process, repeated for 16 steps, generates entanglement between the photon’s polarisation and position.

To model asymmetric behaviour, a loss operator was incorporated, introducing polarization-dependent loss and reducing the probability of detection for one polarisation state relative to the other. By adjusting the loss parameter, scientists investigated how asymmetry impacts the walker’s probability distribution and the robustness of both delocalization and coin-position.

At each step, the probability of detecting the photon at a given position was calculated from the probability amplitudes, allowing for analysis of the inverse participation ratio. This ratio serves as a measure of localization, with values near one indicating localization and values approaching 1/N suggesting complete delocalization. Also, the entanglement entropy was calculated to quantify the degree of coin-position entanglement.

Asymmetry and loss modulate delocalization and entanglement in discrete-time quantum walks

Numerical calculations reveal that asymmetric discrete-time quantum walks (DTQWs) exhibit a marked dependence on asymmetry factors, impacting both delocalization and coin-position entanglement. Investigations into the inverse participation ratio and entanglement entropy demonstrate how these metrics respond to variations in coin parameters and polarization-dependent losses, considering both symmetric and asymmetric initial states.

Simulations showed that specific coin settings could simultaneously enhance both delocalization and coin-position entanglement. At a 16-step implementation, introducing asymmetric polarization-dependent loss led to a substantial decrease in photon probability on the left side of the walk, while the probability on the right side increased and became more localized.

The impact of loss isn’t uniformly negative; under particular coin parameters, both entanglement and delocalization showed improved durability against polarization-dependent loss. Certain configurations maintained a high degree of entanglement even with the introduction of asymmetric loss, suggesting a potential pathway for strong quantum state preparation.

Calculations of the inverse participation ratio provided insight into the spread of the quantum walker, while the entanglement entropy quantified the degree of hybrid entanglement between the coin and position degrees of freedom. The choice of initial state plays a key role in optimising these properties. By selecting an asymmetric initial state, researchers were able to achieve simultaneous enhancement of both coin-position entanglement and delocalization.

The degree of enhancement is sensitive to the specific coin parameters employed, requiring careful tuning to maximise performance. A time-multiplexing fibre loop structure was used to implement the 16-step asymmetric DTQW, allowing for precise control over the walker’s internal states and effective expansion of the accessible position space. By varying the coin parameters, the researchers observed that the system could be tuned to exhibit improved robustness against asymmetric polarization-dependent loss.

At specific settings, the system maintained a high level of delocalization and entanglement despite the presence of loss, indicating a potential for practical applications in quantum information processing. For example, the study showed that the system could maintain a significant degree of entanglement even with a 1.08% polarization-dependent loss, a level that would typically disrupt entanglement in other quantum walk implementations.

Asymmetric photonic walks simultaneously enhance light spread and localisation

Scientists have long sought ways to control the movement of particles with precision, a challenge central to areas like quantum computing and materials science. Recent work detailing asymmetric discrete-time walks offers a new degree of control over photonic delocalization, a phenomenon where light spreads out in a predictable yet potentially useful manner.

Achieving both enhanced spread and focused positioning simultaneously proved difficult, often requiring trade-offs in experimental setups. Researchers have demonstrated a method to boost both characteristics within a single system, utilising asymmetries in the way photons traverse a fibre optic loop. The implications extend beyond simply moving light around.

Understanding and manipulating delocalization is vital for designing more efficient light-harvesting systems, potentially improving solar cell technology. Beyond energy, this level of control could underpin new types of sensors and imaging techniques, where the precise spread of photons is key to resolution and sensitivity. The current experiment relies on a relatively small number of steps in the walk, limiting its complexity and potential for scaling up.

Once larger, more complex walks are realised, the system’s behaviour under more realistic conditions, including imperfections in the fibre optics, needs careful examination. The robustness observed against certain types of signal loss is particularly encouraging. Unlike many quantum systems which are easily disrupted by noise, this setup showed a surprising durability, maintaining performance even with some degree of photon attrition.

The dependence on specific coin parameters, the settings that dictate the direction of the photon’s movement, highlights a limitation. Future work might explore methods to broaden the range of acceptable parameters, making the system more adaptable and less sensitive to calibration. Further investigations into combining these asymmetric walks with other quantum phenomena are anticipated, potentially creating hybrid systems with even more sophisticated functionalities.