Universal Protection of Quantum States from Decoherence

Abstract

The fragility of quantum coherence fundamentally limits the scalability of quantum technologies, as unavoidable environmental interactions induce decoherence and rapidly degrade quantum properties. The Quantum Zeno Effect offers a powerful route to suppress quantum evolution and protect coherence through frequent measurements, irrespective of the underlying dynamics. However, existing implementations require prior knowledge of the quantum state, severely restricting their applicability. Here we introduce a state- and dynamics-independent protection protocol embedding the system in a larger Hilbert space, temporarily swapping the quantum information from its original degree of freedom to a decoherence-free ancillary one. We experimentally validate the protocol on a quantum optical platform, demonstrating robust preservation of coherence and purity for arbitrary polarization qubits under decoherence, thereby enabling the universal safeguarding of unknown quantum states.

Figures (4)

• Figure 1: Quantum State Universal Protection protocol. Quantum circuit representation with CPTP and CP maps: (a) $\Sigma$, describing the evolution of a qubit through a decoherence channel; (b) $\Sigma_\psi$, modeling the evolution of a known qubit $\ket\psi$ through a decoherence channel with its state protected via the Quantum Zeno Effect (QZE); (c) $\Sigma_p$, realizing the protection of an unknown qubit state using the QSUP protocol with general protection map.
• Figure 2: Single-photon-based implementation of Quantum State Universal Protection (QSUP). Experimental scheme of our quantum channel with (lower sketch) and without (upper sketch) QSUP. For the QSUP protocol, Alice encodes a single-photon qubit in its polarization DoF, sending it to a Mach-Zehnder-like interferometer (MZI). There, the SWAP operator between the qubit and the ancilla (here, the MZI path DoF) in Fig. \ref{['scheme']}(c) is realized by a polarizing beam-splitter (PBS) followed by one half-wave plate (HWP) in each arm, rotating both polarization components onto the $\ket\xi$ state to be QZE-protected. In the channel, two HWPs (one per arm) set the basis of the qubit-environment coupling $\{\ket\phi,\ket{\phi^\perp}\}$. Such coupling is implemented by a series of discrete birefringence-based (tiny) decoherence blocks, interspersed by polarizers performing QZE-projections onto the state $\ket\xi$ (at the channel output, two identical HWPs counter-rotate the $\{\ket\phi,\ket{\phi^\perp}\}$ basis into the computational one). On Bob's side, a pair of HWPs and a PBS close the MZI re-performing the SWAP, restoring the initially-encoded polarization state. Then, the qubit undergoes quantum state tomography by means of an apparatus constituted by a HWP, a quarter-wave plate (QWP) and a polarizer. The channel without QSUP [Fig. \ref{['scheme']}(a)] is implemented by removing the MZI as well as the polarizers for the QZE, while keeping the same decoherence-inducing elements.
• Figure 3: Performance assessment. Comparison between unprotected and protected transmission of different polarization-encoded qubit states $\ket\psi = \cos(\psi)\,\ket{H} + \sin(\psi)\,\ket{V}$ ($\psi = 20^\circ$, $45^\circ$, $60^\circ$) through a DIQC, considering different protected states $\ket\xi$ ($\xi = 20^\circ$, $45^\circ$, $60^\circ$). Plot (a): Fidelity $\mathcal{F}$ of the qubit state exiting the DIQC with the one entering it, both in the protected and unprotected cases, considering for the QSUP the worst-case scenario of maximal decoherence ($\xi=45^\circ$). (b) Fidelity $\mathcal{F}$ after the QSUP-assisted transmission for three different input states $\ket\psi$ and protected states $\ket\xi$. (c) Purity $\mathcal{P}$ of the qubit state exiting the DIQC with and without QSUP, considering for the QSUP the worst-case scenario of maximal decoherence ($\xi=45^\circ$). (d) Purity $\mathcal{P}$ after the QSUP-assisted transmission in the DIQC for three different input states and qubit-environment couplings. (e) Qubit survival probability $p_{sur}^{\mathrm{QSUP}}$, considering three different input states $\ket\psi$ and protected states $\ket\xi$. The theoretical simulations (black curves) include absorption-due optical losses.
• Figure S1: Detailed experimental scheme. Heralded single photons at 810 nm are generated via degenerate type-II SPDC occurring within a ppKTP crystal. The L$_\text{IN}$ lens collimates the photons along the DIQC, with a 50:50 BS (BS$_\text{IN}$) directing half of the photons to a monitor channel to track source stability during acquisition. For the QSUP protocol implementation, the combination of PBS$_1$ and HWP$_{\text{A}_\text{IN},\text{B}_\text{IN}}$ performs a SWAP from polarization modes to ancillary path modes of the MZI. Up to $N=4$ decoherence blocks per arm, implemented with birefringent crystal pairs (PC$_i$, CC$_i$), couple the photon polarization to the transverse spatial distribution (which simulates the environment DoF), while the POL$_i$ polarizers realize the QZE-protection. Finally, HWP$_{\text{A}_\text{OUT},\text{B}_\text{OUT}}$ and PBS$_2$ recombine the spatial modes restoring the initial qubit polarization state, which is reconstructed via a quantum state tomography apparatus (HWP$_\text{T}$, QWP$_\text{T}$, PBS$_\text{T}$). A stabilization laser at 780 nm, overlapped with the heralded-photon path and then split from it via dichroic mirrors (DM$_\text{IN}$ and DM$_\text{OUT}$, respectively), controls and stabilizes the interferometer. OFC: optical fiber coupler; OI: optical isolator; HWP: half-wave plate; QWP: quarter-wave plate; M: mirror; ppKTP: periodically-poled potassium titanyl phosphate; PBS: polarizing beam splitter; DM: dichroic mirror; SMF: single-mode fiber; L: lens; SPAD: single-photon avalanche diode; POL: polarizer; PID: proportional-integral-derivative controller; PD: photodiode; PC: principal crystal; CC: compensation crystal; BS: beam splitter; RR: retro-reflector; TM: triangular mirror.