Reference frame mismatch among communication parties introduces errors in quantum cryptographic protocols. As the number of participants increases, aligning reference frames becomes increasingly difficult, complicating multipartite quantum cryptographic implementations. Here, we theoretically and experimentally investigate multipartite reference-frame-independent (RFI) quantum cryptographic communication using Greenberger-Horne-Zeilinger (GHZ) states. We generalize the bipartite RFI security parameter $C$ to an $N$ -party parameter $C_N$ and derive the asymptotic secret key rate expressed solely in terms of experimentally accessible quantities. We analyze the key rate under global and local depolarizing noise models and find that increasing the number of parties $N$ enhances robustness against global depolarizing noise while increasing vulnerability to local channel noise. We also present a proof-of-principle experimental demonstration of four-party RFI quantum cryptographic communication using four-photon GHZ states, confirming the reference-frame invariance of both the $C_4$ parameter and the secret key rate under various reference frame rotations.Reference frame mismatch among communication parties introduces errors in quantum cryptographic protocols. As the number of participants increases, aligning reference frames becomes increasingly difficult, complicating multipartite quantum cryptographic implementations. Here, we theoretically and experimentally investigate multipartite reference-frame-independent (RFI) quantum cryptographic communication using Greenberger-Horne-Zeilinger (GHZ) states. We generalize the bipartite RFI security parameter $C$ to an $N$-party parameter $C_N$ and derive the asymptotic secret key rate expressed solely in terms of experimentally accessible quantities. We analyze the key rate under global and local depolarizing noise models and find that increasing the number of parties $N$ enhances robustness against global depolarizing noise while increasing vulnerability to local channel noise. We also present a proof-of-principle experimental demonstration of four-party RFI quantum cryptographic communication using four-photon GHZ states, confirming the reference-frame invariance of both the $C_4$ parameter and the secret key rate under various reference frame rotations.

quant-pharXiv:2606.12284Jun 11, 20260 citations

System–environment dynamics of GHZ-like states in noninertial frames

Tinggui Zhang, Hong Yang, Shao-Ming Fei

arXiv:2212.14536Quantum Information ProcessingSep 2, 20234 citations

Generalized GHZ entanglement states for optimal rotation detection of quantum spin systems using majorana representation

Yousef Mafi, Payman Kazemikhah, Ali Kookani +2 more

Abstract A multitude of engineering and scientific applications require the estimation of an unknown axis’ rotation, known as the reference frame alignment problem. These problems can be categorized using the quantum Cramer–Rao bound. Detecting rotations is typically focused on smaller angles, as errors are more significant in this range. Therefore, selecting the optimal combination of measurement techniques based on a quantum entangled state for a particular setup is a critical step. This paper proposes a linear combination of anticoherence and coherence measures based on the generalized GHZ entanglement states. The anticoherence measures, optimizes the spin system’s average fidelity in detecting rotated states, while the overlap between states in any spin number is minimal. The optimal quantum rotosensors are characterized by the minimal average fidelity given by the overlap before and after averaging over all directions. The individual subsystems’ states have substantial overlap with GHZ states, making the generalized GHZ state the entanglement quantum spin-j state with coherence decay rate ϵ beneficial in finding the optimal rotation detection on noncoherent entanglement state.Abstract A multitude of engineering and scientific applications require the estimation of an unknown axis’ rotation, known as the reference frame alignment problem. These problems can be categorized using the quantum Cramer–Rao bound. Detecting rotations is typically focused on smaller angles, as errors are more significant in this range. Therefore, selecting the optimal combination of measurement techniques based on a quantum entangled state for a particular setup is a critical step. This paper proposes a linear combination of anticoherence and coherence measures based on the generalized GHZ entanglement states. The anticoherence measures, optimizes the spin system’s average fidelity in detecting rotated states, while the overlap between states in any spin number is minimal. The optimal quantum rotosensors are characterized by the minimal average fidelity given by the overlap before and after averaging over all directions. The individual subsystems’ states have substantial overlap with GHZ states, making the generalized GHZ state the entanglement quantum spin-j state with coherence decay rate ϵ beneficial in finding the optimal rotation detection on noncoherent entanglement state.

Physica ScriptaJan 11, 20240 citations

Coherent States as a Tool for Obtaining Rigorous Bounds

Élliott H. Lieb

Springer eBooksJan 1, 20027 citations

Optimal state for keeping reference frames aligned and the platonic solids

Piotr Leszek Kolenderski, Rafał Demkowicz-Dobrzański

The optimal $N$ qubit states featuring highest sensitivity to small misalignment of Cartesian reference frames are found using the quantum Cram\'er-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin $J=N∕2$ . Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.The optimal $N$ qubit states featuring highest sensitivity to small misalignment of Cartesian reference frames are found using the quantum Cram\'er-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin $J=N∕2$. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.

arXiv:0805.3637Physical Review ANov 26, 200864 citations

C

to an

N

-party parameter

C_N

and derive the asymptotic secret key rate expressed solely in terms of experimentally accessible quantities. We analyze the key rate under global and local depolarizing noise models and find that increasing the number of parties

N

enhances robustness against global depolarizing noise while increasing vulnerability to local channel noise. We also present a proof-of-principle experimental demonstration of four-party RFI quantum cryptographic communication using four-photon GHZ states, confirming the reference-frame invariance of both the

C_4

parameter and the secret key rate under various reference frame rotations.

The optimal

N

qubit states featuring highest sensitivity to small misalignment of Cartesian reference frames are found using the quantum Cram\'er-Rao bound. It is shown that the optimal states are supported on the symmetric subspace and hence are mathematically equivalent to a single spin

J=N∕2

. Majorana representation of spin states is used to reveal a beautiful connection between the states optimal for aligning reference frames and the platonic solids.