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Physical Review A

Observation of decoherence-induced exchange symmetry breaking in an entangled state

Hyang‐Tag Lim, Jong Chan Lee, Kang-Hee Hong, Yoon-Ho Kim

Published Nov 24, 2014• 5 citations
Publisher

Abstract

One of the most intriguing features of entanglement is that entangled quantum systems exhibit exchange symmetry; that is, local quantum operations on the subsystems may be interchanged without affecting the quantum state. In this work, we investigate whether the exchange symmetry is preserved for the weak (or partial collapse) measurement, a type of quantum operation, in the presence of decoherence. Demonstrated using two entangled photonic polarization qubits, the experimental results clearly show that the exchange symmetry is broken once decoherence is introduced, even though the photons still share nonzero entanglement. Our results shed light on quantum state manipulation using general quantum operations on entangled quantum states in the presence of decoherence.

DOI
10.1103/physreva.90.052328

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One of the most intriguing features of entanglement is that entangled quantum systems exhibit exchange symmetry; that is, local quantum operations on the subsystems may be interchanged without affecting the quantum state. In this work, we investigate whether the exchange symmetry is preserved for the weak (or partial collapse) measurement, a type of quantum operation, in the presence of decoherence. Demonstrated using two entangled photonic polarization qubits, the experimental results clearly show that the exchange symmetry is broken once decoherence is introduced, even though the photons still share nonzero entanglement. Our results shed light on quantum state manipulation using general quantum operations on entangled quantum states in the presence of decoherence.
We experimentally investigate the variations of exchange-symmetry properties of the four Bell states in an exchange-symmetric pure dephasing process with a two-photon system generated from spontaneous parametric down-conversion (SPDC). Experiment results show that under such an exchange-symmetric local-noise Hamiltonian, the exchange-symmetry property remains unchanged for two of the three symmetric Bell states, i.e., the states $|\ensuremath{\Phi}\ensuremath{\rangle}{}^{\ifmmode\pm\else\textpm\fi{}}=\frac{1}{\sqrt{2}}(|00\ensuremath{\rangle}\ifmmode\pm\else\textpm\fi{}|11\ensuremath{\rangle})$. For the antisymmetric Bell state $|\ensuremath{\Psi}\ensuremath{\rangle}{}^{\ensuremath{-}}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}\ensuremath{-}|10\ensuremath{\rangle})$, the exchange-symmetry property increases and achieves a maximum value of 0.5 at the asymptotic limit. However, for the third exchange-symmetric Bell state $|\ensuremath{\Psi}\ensuremath{\rangle}{}^{+}=\frac{1}{\sqrt{2}}(|01\ensuremath{\rangle}+|10\ensuremath{\rangle})$, the exchange-symmetry property breaks, surviving with a probability of 0.5 at the asymptotic limit, which provides some evidence supporting such decoherence-induced spontaneous-symmetry-breaking phenomena.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
The preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy, yet its stability against realistic, non-commuting measurement noise remains a critical open question. Here, we systematically investigate the rich phase structure emerging from a minimal model of competing, non-commuting weak measurements: nearest-neighbor Ising (ZiZjZ_iZ_jZi​Zj​) and single-qubit transverse (XiX_iXi​) operators. We analyze three experimentally relevant scenarios based on which measurement outcomes are read out: complete readout, no readout, and partial readout. Using a replica mean-field theory for higher dimensions, complemented by numerical simulations in one dimension, we derive the complete finite-time and stationary phase diagrams. Our analysis reveals a striking dependence on the readout protocol. Complete readout yields a direct transition between a short-range entangled (SRE) phase and a pure LRE phase. No readout (pure decoherence) precludes entanglement but exhibits a strong-to-weak spontaneous symmetry breaking (SWSSB) transition into a classically ordered mixed state. Most intriguingly, partial readout interpolates between these limits, featuring a mixed-state phase transition where the system can become trapped in the SWSSB phase or, for weaker non-commutativity, undergo successive symmetry breaking to reach a mixed LRE phase. A novel technical contribution is the use of a channel-fidelity-based partition function that allows us to simultaneously characterize both entanglement and SWSSB order, revealing a deep interplay between them in the replica limit. These results provide a cohesive picture for understanding measurement phase transitions, SWSSB, and mixed-state phase transitions, offering crucial insights for designing robust state preparation protocols on noisy quantum devices.
We discuss the cases where local decoherence selectively degrades one type of entanglement more than other types. A typical case is called state ordering change, in which two input states with different amounts of entanglement undergoes a local decoherence and the state with the larger entanglement results in an output state with less entanglement than the other output state. We are also interested in a special case where the state with the larger entanglement evolves to a separable state while the other output state is still entangled, which we call selective entanglement breaking. For three-level or larger systems, it is easy to find examples of the state ordering change and the selective entanglement breaking, but for two-level systems it is not trivial whether such situations exist. We present a general strategy to construct examples of two-qubit states exhibiting the selective entanglement breaking regardless of entanglement measure. We also give a more striking example of the selective entanglement breaking in which the less entangled input state has only an infinitesimal amount of entanglement.
Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_{n} symmetry-breaking transitions for both cases. In the case of Z_{2}, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.