Exchange Symmetry in Multiphoton Quantum Interference

Abstract: Photons are bosons, and yet, when prepared in specific entangled states, they can exhibit non-bosonic behaviour. While this phenomenon has so far been studied in two-photon systems, exchange symmetries and interference effects in multi-photon scenarios remain largely unexplored. In this work, we show that multi-photon states uncover a rich landscape of exchange symmetries. With three photons already, multiple pairwise combinations are possible, where each pair of photons can exhibit either bosonic, fermionic, or anyonic exchange symmetry. This gives rise to mixed symmetry systems that are not possible to achieve with two photon alone. We experimentally investigate how these symmetry configurations manifest themselves in the observed interference of three photons. We show that multi-photon interference can be effectively turned on and off by tuning the symmetry of the constituent pairs. The possibility of accessing and tuning new quantum statistics in a scalable photonic platform not only deepens our understanding of quantum systems, but is also highly relevant for quantum technologies that rely on quantum interference.

• The paper introduces a phase-tuned three-photon state that interpolates between symmetric and mixed-symmetry regimes to control multiphoton interference.
• It employs a sophisticated experimental setup using SPDC sources, variable beam splitters, and high HOM visibilities to verify state fidelity.
• Results show that varying the phase parameter φ modulates scattering statistics, paving the way for simulating non-bosonic quantum statistics in scalable photonic systems.

Exchange Symmetry Effects in Multiphoton Quantum Interference

Introduction

The paper "Exchange Symmetry in Multiphoton Quantum Interference" (2512.07953) explores foundational aspects of quantum interference originating from exchange symmetry properties of bosonic photons. Traditionally, the bosonic exchange symmetry necessitates symmetric wavefunctions under particle exchange, dictating phenomena such as photon bunching and the absence of the Pauli exclusion principle for photons. This study extends known two-photon results to three-photon systems, revealing a much richer landscape of symmetry through pairwise and mixed-exchange symmetries. The work demonstrates, both theoretically and experimentally, how tuning the symmetry via internal and external degrees of freedom can control interference signatures, thus opening avenues for manipulating quantum statistics in scalable photonic architectures.

Figure 1: Probing exchange symmetry in photon interference: (a) The bosonic symmetry of the wavefunction for $N$ photons can be distributed over different degrees of freedom, granting access to non-bosonic pairwise exchange statistics upon evolution and measurement. (b) Three-photon state with tunable relative phase $\phi$ directly controls exchange symmetry.

Theoretical Framework

The central construct is a parametrized three-photon state $\ket{\Psi^{\phi}_{a,a,b}}$ configured across spatial modes $a$ and $b$ and polarizations $\ket{0},\ket{1}$. By adjusting a phase parameter $\phi$, the authors interpolate between pure symmetric and mixed-symmetry states:

• Symmetric state: All pairwise exchanges yield symmetric contributions.
• Mixed-symmetry state: One photon pair exhibits symmetry, the other anti-symmetry.

These basis states are superpositions:

$$\ket{\Psi^{\phi}_{a,a,b}} = \cos(\phi/2)\ket{\Psi}_{a,a,b}^{\mathrm{sym}} - i\sin(\phi/2)\ket{\Psi}_{a,a,b}^{\mathrm{mix}}$$

with the weights explicitly controlling statistical symmetry types.

Scattering probabilities for various photon output layouts at a variable beam splitter (VBS), characterized by a tunable ratio parameter $\theta$, are derived. Crucially, the fully-bunched outcomes only result from the symmetric state and are suppressed for mixed-symmetry configurations (anti-symmetry imposes effective fermionic behavior).

Experimental Implementation

A sophisticated scheme achieves the required three-photon input state. The setup involves:

• Photon Sources: SPDC-based linear and Sagnac sources produce heralded single photons and tunable Bell states.
• State Preparation: The single photon and one Bell photon are interfered at a 50:50 beam splitter, post-selecting successful mode coalescence.
• Variable Beam Splitter and Detection: Outputs of the VBS feed into four-fold demultiplexed SNSPD arrays, leveraging pseudo photon-number resolution.

  Figure 2: Experimental schematic involving SPDC sources for single photon and Bell states, post-selected at a balanced beam splitter and analyzed via a fiber-based variable beam splitter.

Hong-Ou-Mandel (HOM) interference visibilities ($99.3^{+0.5}_{-0.6}\%$ Sagnac source; $95.4^{+3.1}_{-4.5}\%$ dual-source) were quantified to confirm photonic indistinguishability and the fidelity of prepared states.

Results

Scattering statistics for single photons, generalized Bell states, their products, and three-photon entangled states were measured for multiple $\phi$ values. Notable findings include:

• For $\phi=0$, joint three-photon statistics diverge substantially from the product of two-photon and single-photon statistics, capturing genuine three-photon interference.
• As $\phi$ increases toward $\pi/2$, intermediate deviations indicate gradually diminishing interference.
• At $\phi=\pi$, joint and product statistics converge, signifying the effective absence of multiphoton interference: the anti-symmetry forcibly suppresses three-photon bunching.

  Figure 3: Scattering probabilities as functions of VBS parameter $\theta$ for different photonic input states and phase $\phi$, with clear distinction between joint and product statistics attesting to multi-photon interference signatures.

  

  Figure 4: Experimental realization of scattering statistics for three-photon states, Bell states, single photons, and their statistical products across the full range of $\phi$, including the explicit calculation of deviations $\Delta P$.

Systematic agreement between theoretical predictions and experiment was achieved, modulo minor discrepancies attributed to non-ideal source preparation, finite spectral mismatch, VBS hysteresis, and detection Poissonian errors.

Practical and Theoretical Implications

This study demonstrates tunable multi-photon interference controlled by the symmetry of constituent states, providing a route to simulate non-bosonic quantum statistics (including anyonic and immanonic regimes) using photons. The ability to program the underlying symmetry directly impacts experimental protocols in quantum simulation, quantum walks, and photonic quantum information processing.

The results illuminate the interplay between internal and external degrees of freedom in composing global wavefunction symmetry and suggest scaling pathways to larger multipartite systems where complex exchange statistics could be engineered. The exploration of generalized statistics (immanons) extends the framework beyond the perennial determinant/permanent dichotomy, offering new directions for quantum algorithm implementation and error correction paradigms.

Prospects for Future Research

The findings invite further work on:

• Scaling to larger photon numbers and higher-dimensional states (qutrits, ququads) to emulate more complex quantum particles.
• Developing programmable photonic circuits for dynamically tuning exchange symmetry in real-time.
• Exploration of simulated anyonic or fractional statistics for topological quantum computation.
• Investigating decoherence and robustness of engineered symmetry states under realistic noise and loss.

Conclusion

This paper provides a systematic investigation into the control and observation of exchange symmetry effects in multi-photon interference. Through phase-tuned state preparation, it is possible to switch multi-photon interference on and off, fundamentally distinguishing pure bosonic from mixed-symmetry regimes. These results underpin scalable photonic quantum technologies where symmetry properties can be harnessed as computational resources, and provide a template for future extensions into more exotic quantum statistical domains.