What does it mean for a mixed-state topological phase to be chiral? Mathematically, chirality can be sharply characterized through the symmetry algebra of the mixed state. Physically, however, the question is far more subtle. In pure states, chirality in topological phase is tied to a web of familiar diagnostics, involving bulk-boundary correspondence, a gapless entanglement spectrum, a nontrivial modular commutator, and a quantized thermal Hall response. We show that none of these diagnostics remain reliable in mixed states. Instead, for decohered topological phases with a known error-free parent state, we propose two relative-entropy-based measures that can diagnose chirality, with one of them further extracting the chiral central charge. As a concrete example, we use these measures to analyze the
em2-decohered
Z3 toric code, identifying the chirality transition to be in the random-bond Potts class for the particle-hole symmetric channel, and the polarized random bond Potts class for asymmetric channels. Our results emphasize how mixed-state topology demands intrinsically new diagnostics beyond direct analogues of pure-state probes.
Abstract In this paper, we investigate the decay of entanglement of multiqubit randomized entangled states. We start by introducing separable states of collection of n independent qubits. The randomized entangled mixed states are generated from factorisable initial states by coupling the qubits through randomized entangling operators. The bipartite and multipartite entanglement of randomized states are analyzed by employing respectively the concepts of the negativity and the genuine multiparticle negativity as measures of amount of entanglement. The decreases of the amount of entanglement of randomized entangled mixed states is studied in terms of the noisy parameter p .
Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born's rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.