A computable measure of entanglement is introduced, which can be effectively computed for any mixed state of an arbitrary bipartite system. This measure, called negativity, is defined as half the difference between the trace norm of the partial transpose of the state and 1. It is shown to be an entanglement monotone, meaning it does not increase under local operations and classical communication (LOCC). The logarithmic negativity, defined as the logarithm of the trace norm of the partial transpose, is also introduced and shown to be additive and monotonic under LOCC. The negativity provides a lower bound on the teleportation capacity of a mixed state, quantifying how close it can be made to a maximally entangled state using LOCC. It also bounds the distillable entanglement of a mixed state, which is the amount of entanglement that can be asymptotically distilled from multiple copies of the state. The logarithmic negativity is shown to be an upper bound on the distillable entanglement. The paper also discusses the application of these measures to various classes of states, including pure states, symmetric mixed states, and Gaussian states of light fields. For pure states, the negativity is shown to be related to the robustness of entanglement. For symmetric mixed states, the negativity is computed explicitly in terms of parameters that characterize the state. For Gaussian states, the negativity is computed using the symplectic spectrum of the covariance matrix, which is derived from the normal mode decomposition of the state. The results show that the negativity and logarithmic negativity are effective measures of entanglement that can be computed efficiently for mixed states. They provide bounds on the teleportation capacity and distillable entanglement of mixed states, and have applications in the study of entanglement in multipartite systems. The paper concludes that these measures are important tools for understanding entanglement in quantum systems.A computable measure of entanglement is introduced, which can be effectively computed for any mixed state of an arbitrary bipartite system. This measure, called negativity, is defined as half the difference between the trace norm of the partial transpose of the state and 1. It is shown to be an entanglement monotone, meaning it does not increase under local operations and classical communication (LOCC). The logarithmic negativity, defined as the logarithm of the trace norm of the partial transpose, is also introduced and shown to be additive and monotonic under LOCC. The negativity provides a lower bound on the teleportation capacity of a mixed state, quantifying how close it can be made to a maximally entangled state using LOCC. It also bounds the distillable entanglement of a mixed state, which is the amount of entanglement that can be asymptotically distilled from multiple copies of the state. The logarithmic negativity is shown to be an upper bound on the distillable entanglement. The paper also discusses the application of these measures to various classes of states, including pure states, symmetric mixed states, and Gaussian states of light fields. For pure states, the negativity is shown to be related to the robustness of entanglement. For symmetric mixed states, the negativity is computed explicitly in terms of parameters that characterize the state. For Gaussian states, the negativity is computed using the symplectic spectrum of the covariance matrix, which is derived from the normal mode decomposition of the state. The results show that the negativity and logarithmic negativity are effective measures of entanglement that can be computed efficiently for mixed states. They provide bounds on the teleportation capacity and distillable entanglement of mixed states, and have applications in the study of entanglement in multipartite systems. The paper concludes that these measures are important tools for understanding entanglement in quantum systems.