Exchange-Symmetrized Qudit Bell Bases and Bell-State Distinguishability

Abstract

Entanglement of qudit pairs, with single particle Hilbert space dimension $d$, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension $d$, we introduce a generalized Bell basis with definite symmetry under exchange of internal states between the two particles. We show that no complete exchange-symmetrized basis can exist for odd $d$. This framework extends prior work on exchange-symmetrized hyperentangled qubit bases, where $d$ is a power of two. For our exchange-symmetrized basis we show that measurement devices restricted to linear evolution and local measurement (LELM) can unambiguously distinguish $2d-1$ qudit Bell states for any even $d$. This achieves the upper bound in general for reliable Bell-state distinguishability via LELM and augments previously known limits for $d=2^n$ and $d=3$. This result is relevant to near-term realizations of quantum communication protocols.

References in corpus (17)

• Experimental quantum teleportation
• Quantum algorithm for solving linear systems of equations
• Beating the channel capacity limit for linear photonic superdense coding
• Experimental demonstration of four-party quantum secret sharing
• Hyperentangled Bell-state analysis
• Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ansätze
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings
• Mutually unbiased bases and generalized Bell states
• Noisy Qudit vs Multiple Qubits : Conditions on Gate Efficiency for Enhancing Fidelity
• Deterministic generation of qudit photonic graph states from quantum emitters
• Demonstrating experimentally the encoding and dynamics of an error-correctable logical qubit on a hyperfine-coupled nuclear spin qudit
• Simple criterion for local distinguishability of generalized Bell states in prime dimension
• Local discrimination of generalized Bell states via commutativity
• Symmetric extendibility for qudits and tolerable error rates in quantum cryptography
• Symmetry Protected Quantum Computation
• Enhanced Bell state measurement for efficient measurement-device-independent quantum key distribution using 3-dimensional quantum states

Cited by in corpus (1)

• Classical representation of local Clifford operators