Permutation invariance in quantum processes

The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak-, strong-, and ultrastrong-coupling regimes. Using PIQS, we reproduce a series of known physical results concerning collective quantum effects and extend their study to the local driven-dissipative scenario. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, and quantum phase transitions, against local dissipation processes.The permutational invariance of identical two-level systems allows for an exponential reduction in the computational resources required to study the Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of both local and collective noise. Here we take advantage of this speedup to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir. Assessing the robustness of collective effects against local dissipation is paramount to predict their presence in different physical implementations. We have developed an open-source library in python, the Permutational-Invariant Quantum Solver (PIQS), which we use to study a variety of phenomena in driven-dissipative open quantum systems. We consider both local and collective incoherent processes in the weak-, strong-, and ultrastrong-coupling regimes. Using PIQS, we reproduce a series of known physical results concerning collective quantum effects and extend their study to the local driven-dissipative scenario. Our work addresses the robustness of various collective phenomena, e.g., spin squeezing, superradiance, and quantum phase transitions, against local dissipation processes.

arXiv:1805.05129Physical Review ADec 10, 2018245 citations

A state-space approach to quantum permutations

J.P. McCarthy

Expositiones MathematicaeDec 30, 20213 citations

Quantum processes on phase space

Charis Anastopoulos

arXiv:quant-ph/0205132Annals of PhysicsFeb 1, 200326 citations

Quantum Anonymous Secret Sharing with Permutation Invariant Codes

Varin Sikand, Andrew Nemec

Quantum secret sharing schemes are a family of quantum cryptographic protocols which provide secure quantum encodings, mapping one secret to multiple shares of information such that the original secret cannot be accessed without an authorized set of shares present for decoding. In this work, we describe a protocol that enables sender-anonymity during the secret decoding process. By using permutation-invariant QEC codes along with a set of anonymous quantum transmission algorithms, we construct a quantum anonymous secret sharing scheme that achieves sender-anonymity. We quantify information leakage in ramp quantum secret sharing schemes via the quantum conditional min-entropy, justifying it as a valid measure of leaked information by relating it to the Knill-Laflamme quantum error correction conditions. Finally, we evaluate several permutation-invariant codes using this measure to make observations on the information leakage of intermediate shares for each quantum anonymous secret sharing scheme.Quantum secret sharing schemes are a family of quantum cryptographic protocols which provide secure quantum encodings, mapping one secret to multiple shares of information such that the original secret cannot be accessed without an authorized set of shares present for decoding. In this work, we describe a protocol that enables sender-anonymity during the secret decoding process. By using permutation-invariant QEC codes along with a set of anonymous quantum transmission algorithms, we construct a quantum anonymous secret sharing scheme that achieves sender-anonymity. We quantify information leakage in ramp quantum secret sharing schemes via the quantum conditional min-entropy, justifying it as a valid measure of leaked information by relating it to the Knill-Laflamme quantum error correction conditions. Finally, we evaluate several permutation-invariant codes using this measure to make observations on the information leakage of intermediate shares for each quantum anonymous secret sharing scheme.

quant-pharXiv:2604.27284May 1, 20260 citations

Decomposition of a symmetric multipartite observable

You Zhou, Chenghao Guo, Xiongfeng Ma

Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under permutations between parties, with only $(N+1)(N+2)/2$ local measurement settings, where $N$ is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations, $m$ , we derive a tight linear bound on the number of local measurement settings, $m(2m+3)N+1$ . Meanwhile, for the Greenberger-Horne-Zeilinger state, the $W$ state, and the Dicke state, we prove a linear lower bound, $\mathrm{\ensuremath{\Theta}}(N)$. Hence, for these particular states, our decomposition technique is optimal.Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under permutations between parties, with only $(N+1)(N+2)/2$ local measurement settings, where $N$ is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations, $m$, we derive a tight linear bound on the number of local measurement settings, $m(2m+3)N+1$. Meanwhile, for the Greenberger-Horne-Zeilinger state, the $W$ state, and the Dicke state, we prove a linear lower bound, $\mathrm{\ensuremath{\Theta}}(N)$. Hence, for these particular states, our decomposition technique is optimal.

arXiv:1902.07496Physical Review AMay 16, 201911 citations

Systems of covariance in quantum probability

Stanley Gudder

International Journal of Theoretical PhysicsMay 1, 19920 citations

(N+1)(N+2)/2

local measurement settings, where

N

is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations,

m

, we derive a tight linear bound on the number of local measurement settings,

m(2m+3)N+1

. Meanwhile, for the Greenberger-Horne-Zeilinger state, the

W

state, and the Dicke state, we prove a linear lower bound, $\mathrm{\ensuremath{\Theta}}(N)$. Hence, for these particular states, our decomposition technique is optimal.