When is there a multipartite maximum entangled state?

For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes... d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em maximum} in the sense that all other states in the system can be obtained from the state through local quantum operations and classical communications (LOCC)? When $d_1\ge\Pi_{i=2}^n d_i$, such state exists. We show that this condition is also necessary. Our proof, somewhat surprisingly, uses results from algebraic complexity theory.Comment: 10 pages, no figure. We know the answer is quite simple, but the proof is somewhat involved. Comments are welcom

Entanglement between Two Uses of a Noisy Multipartite Quantum Channel Enables Perfect Transmission of Classical Information

Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and is enabled by quantum entanglement.Comment: 5 pages (actually 4 pages and a bit more, in Revtex 4), 1 eps. Comments are welcome. Don't miss a related work arXiv:0712.362

Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations

Deletion of heat shock protein 60 in adult mouse cardiomyocytes perturbs mitochondrial protein homeostasis and causes heart failure.

To maintain healthy mitochondrial enzyme content and function, mitochondria possess a complex protein quality control system, which is composed of different endogenous sets of chaperones and proteases. Heat shock protein 60 (HSP60) is one of these mitochondrial molecular chaperones and has been proposed to play a pivotal role in the regulation of protein folding and the prevention of protein aggregation. However, the physiological function of HSP60 in mammalian tissues is not fully understood. Here we generated an inducible cardiac-specific HSP60 knockout mouse model, and demonstrated that HSP60 deletion in adult mouse hearts altered mitochondrial complex activity, mitochondrial membrane potential, and ROS production, and eventually led to dilated cardiomyopathy, heart failure, and lethality. Proteomic analysis was performed in purified control and mutant mitochondria before mutant hearts developed obvious cardiac abnormalities, and revealed a list of mitochondrial-localized proteins that rely on HSP60 (HSP60-dependent) for correctly folding in mitochondria. We also utilized an in vitro system to assess the effects of HSP60 deletion on mitochondrial protein import and protein stability after import, and found that both HSP60-dependent and HSP60-independent mitochondrial proteins could be normally imported in mutant mitochondria. However, the former underwent degradation in mutant mitochondria after import, suggesting that the protein exhibited low stability in mutant mitochondria. Interestingly, the degradation could be almost fully rescued by a non-specific LONP1 and proteasome inhibitor, MG132, in mutant mitochondria. Therefore, our results demonstrated that HSP60 plays an essential role in maintaining normal cardiac morphology and function by regulating mitochondrial protein homeostasis and mitochondrial function