Eyuri Wakakuwa

Markovianizing Cost of Tripartite Quantum States

We introduce and analyze a task that we call Markovianization, in which a tripartite quantum state is transformed to a quantum Markov chain by a randomizing operation on one of the three subsystems. We consider cases where the initial state is the tensor product of

The chain rule implies Tsirelson's bound: an approach from generalized mutual information

n

Asymptotic convertibility of entanglement: An information-spectrum approach to entanglement concentration and dilution

copies of a tripartite state

The Cost of Randomness for Converting a Tripartite Quantum State to be Approximately Recoverable

\rho^{ABC}

A coding theorem for bipartite unitaries in distributed quantum computation

, and is transformed to a quantum Markov chain conditioned by

A Four-Round LOCC Protocol Outperforms All Two-Round Protocols in Reducing the Entanglement Cost for A Distributed Quantum Information Processing

B^n

A Coding Theorem for Bipartite Unitaries in Distributed Quantum Computation

with a small error, using a random unitary operation on

Markovianizing cost of tripartite quantum states

A^n

Conditional quantum one-time pad.

. In an asymptotic limit of infinite copies and vanishingly small error, we analyze the Markovianizing cost, that is, the minimum cost of randomness per copy required for Markovianization. For tripartite pure states, we derive a single-letter formula for the Markovianizing costs. Counterintuitively, the Markovianizing cost is not a continuous function of states, and can be arbitrarily large even if the state is close to a quantum Markov chain. Our results have an application in analyzing the cost of resources for simulating a bipartite unitary gate by local operations and classical communication.

Operational Resource Theory of Non-Markovianity

In order to analyze an information theoretical derivation of Tsirelsons bound based on information causality, we introduce a generalized mutual information (GMI), defined as the optimal coding rate of a channel with classical inputs and general probabilistic outputs. In the case where the outputs are quantum, the GMI coincides with the quantum mutual information. In general, the GMI does not necessarily satisfy the chain rule. We prove that Tsirelsons bound can be derived by imposing the chain rule on the GMI. We formulate a principle, which we call the no-supersignaling condition, which states that the assistance of nonlocal correlations does not increase the capability of classical communication. We prove that this condition is equivalent to the no-signaling condition. As a result, we show that Tsirelsons bound is implied by the nonpositivity of the quantitative difference between information causality and no-supersignaling.