Barbara M. Terhal

Remote State Preparation

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit--half that of teleportation--and even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.

Unextendible product bases and bound entanglement

An unextendible product basis( UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the subspace complementary to any UPB is a bound entangled state. We exhibit a tripartite 2 3 2 3 2 UPB whose complementary mixed state has tripartite entanglement but no bipartite entanglement, i.e., all three corresponding 2 3 4 bipartite mixed states are unentangled. We show that members of a UPB are not perfectly distinguishable by local positive operator valued measurements and classical communication. [S0031-9007(99)09360-6]

Bell inequalities and the separability criterion

Abstract We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for entanglement. We also show how the criterion for separability and the existence of a description of the state by a local hidden variable theory, become equivalent when we restrict the set of local hidden variable theories to the domain of quantum mechanics. This analysis sheds light on the essential difference between the two criteria.

Quantum data hiding

We expand on our work on quantum data hiding - hiding classical data among parties who are restricted to performing only local quantum operations and classical communication (LOCC). We review our scheme that hides one bit between two parties using Bell (1964) states, and we derive upper and lower bounds on the secrecy of the hiding scheme. We provide an explicit bound showing that multiple bits can be hidden bitwise with our scheme. We give a preparation of the hiding states as an efficient quantum computation that uses at most one ebit of entanglement. A candidate data-hiding scheme that does not use entanglement is presented. We show how our scheme for quantum data hiding can be used in a conditionally secure quantum bit commitment scheme.

The asymptotic entanglement cost of preparing a quantum state

We give a detailed proof of the conjecture that the asymptotic entanglement cost of preparing a state ρ is equal to limn→∞ Ef (ρ ⊗n )/n where Ef is the entanglement of formation.

Schmidt number for density matrices

We introduce the notion of a Schmidt number of a bipartite density matrix. We show that k-positive maps witness the Schmidt number, in the same way that positive maps witness entanglement. We determine the Schmidt number of the family of states that is made from mixing the completely mixed state and a maximally entangled state. We show that the Schmidt number does not necessarily increase when taking tensor copies of a density matrix

Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

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Detecting quantum entanglement

we give an example of a density matrix for which the Schmidt numbers of

Locking Classical Correlations in Quantum States

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Entanglement of formation for isotropic states

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