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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…
The complexity of quantum spin systems on a two-dimensional square lattice
It is obtained that quantum adiabatic computation using 2-local interactions restricted to a 2-D square lattice is equivalent to the circuitmodel of quantum computation.
Quantum error correction for quantum memories
- B. Terhal
- 14 February 2013
It may seem inevitable that highly entangled quantum states are susceptible to disturbance through interaction with a decohering environment. However, certain multiqubit entangled states are well…
Classical simulation of noninteracting-fermion quantum circuits
It is shown that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension.
The complexity of stoquastic local Hamiltonian problems
It is proved that LH-MIN for stoquastic Hamiltonians belongs to the complexity class AM -- a probabilistic version of NP with two rounds of communication between the prover and the verifier, and that any problem solved by adiabatic quantum computation using stoquian Hamiltonians is in PostBPP.
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
It is demonstrated that a self-correcting quantum memory cannot be built using stabilizer codes in dimensions D=1, 2, in sharp contrast with the existence of a classical self- correcting memory in the form of a two-dimensional (2D) ferromagnet.
The entanglement of purification
We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to…
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…
Complexity of Stoquastic Frustration-Free Hamiltonians
The Cook-Levin theorem proving NP-completeness of the satisfiability problem is generalized to the complexity class MA (Merlin-Arthur games)—a probabilistic analogue of NP.
Quantum data hiding
It is proved that the information that Alice and Bob can gain about a hidden bit is exponentially small in n, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits.