Peter Shor

“Quantum state restoration extends a large subsystem of a single-copy n-qubit state |ψ⟩ to the full state efficiently, given a verification procedure.”

“The codes are nonadditive and exploit self-complementarity structure”

“All constructed quantum amplitude damping codes are nonadditive”

“Specific 3SAT instances with two planted solutions penalized by one clause are not solved efficiently by the simplest quantum adiabatic algorithm.”

“Quantum error recovery can be optimized to maximize entanglement fidelity for a specific input state and noise model instead of perfect correction on error subsets.”

“Generalized concatenation constructs both stabilizer and nonadditive quantum codes”

“Good quantum error-correcting codes can be constructed using generalized concatenation.”

“Amplitude damping errors can be analyzed in the stabilizer formalism”

“For channels of nonzero capacity, simulation of a noisy channel by a noiseless one is always possible.”

“The protocol improves entanglement purification for bipartite mixed states”

“iTEBD algorithm is generalized to simulate quantum spin systems on infinite tree geometries.”

“The maximum trace distance between a PPT state and the set of separable states tends to 1 as the dimension of the Hilbert space tends to infinity.”

“Evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is complete for the one clean qubit complexity class”

“Every stabilizer code is locally equivalent to a graph code”

“A new protocol achieves a higher quantum communication rate over the erasure channel with backward classical communication than the best prior result.”

“The quantum clique problem is QMA-complete.”

“Public-key quantum money allows a bank to create quantum states that anyone can verify but no one except possibly the bank can clone or forge.”

“Coherent information is an achievable rate for entanglement transmission through noisy quantum channels.”

“Verifier confirms n-size 3SAT satisfiability with constant soundness using ~O(sqrt(n)) unentangled quantum witnesses of O(log n) qubits each”

“Any C3 gate is a generalized semi-Clifford operator”

“The family of protocols generalizes four previous methods: recurrence method, modified recurrence method, Maneva-Smolin, and Leung-Shor.”

“Semidefinite programming (SDP) computes the optimal quantum recovery operation maximizing average entanglement fidelity for a given encoding and channel model.”

“The adaptive capacity C_{1,A} lies strictly between C_{1,1} and C_{1,infinity} for three symmetric pure states in three dimensions.”

“Universal quantum computation can be achieved adiabatically using 2-local Hamiltonians”

“The classical capacity of a quantum channel with limited entanglement assistance forms a continuous trade-off curve between the unassisted HSW capacity and the entanglement-assisted capacity.”

“The entanglement-assisted capacity of a multimode bosonic lossy channel is explicitly calculated.”

“Concatenated codes provide non-zero capacity for depolarizing channels when fidelity f > 0.80944”

“BB84 protocol is unconditionally secure for quantum key distribution.”

“A family of packings exists with (m² + m - 2) subspaces of dimension m/2 in m-dimensional space”

“A group theoretic framework simplifies known quantum error-correcting codes and facilitates new constructions”

“Unitary gates exhibit dramatic separations between forward and backward capacities”

“Quantum algorithms exist that solve certain problems significantly faster than corresponding classical algorithms.”

“The minimum entropy of the output is additive for the tensor product of an entanglement-breaking quantum channel and an arbitrary quantum channel.”

“Remote state preparation requires 1 bit of classical communication and 1 bit of entanglement per qubit for arbitrary many-qubit states.”

“Every good quantum error-correcting code discovered prior to this work is a stabilizer code, defined as an eigenspace of an Abelian group generated by tensor products of Pauli matrices”

“Additivity of the minimum output entropy of a quantum channel is equivalent to additivity of the Holevo expression for classical channel capacity”

“There exist discrete memoryless quantum channels where Q_2 > C_H”

“Totally isotropic subspaces in Ω⁺(2i,2) generate infinite families of packings of 2^k-dimensional subspaces in ℝ^{2^i}”

“Finding quantum error-correcting codes is equivalent to finding additive codes over GF(4) that are self-orthogonal with respect to a trace inner product.”

“A two-parameter family of bipartite mixed states ρ_bc exists in d⊗d Hilbert space that are NPT.”

“Two non-distillable bound-entangled states, when tensored in a multi-party setting, form a distillable state.”

“Perfectly secure private quantum channel in dimension d requires 2 log d shared random key bits.”

“Oblivious RSP protocols for basis-forming pure state projectors can be modified to require only a single specimen of the state from the sender.”

“A relationship exists between entanglement fidelity and average fidelity for a completely depolarizing quantum channel.”

“Entanglement-breaking channels can always be written in the canonical form introduced by Holevo.”

“Previous quantum error-correcting codes fail for noise introducing more than one bit of entropy per qubit.”

“SS algorithm runs in O(nB) time for integral bin capacity B and n items.”

“An unextendible product basis (UPB) is an incomplete orthogonal product basis whose complementary subspace contains no product state”

“An expression characterizes all admissible rate pairs (R_c, R_q) for simultaneous classical and quantum information transmission over any quantum channel.”

“Entanglement-assisted classical capacity C_EA(N) = max_ρ [H(ρ) + H(N(ρ)) - H(ρ, N(ρ))], with joint entropy from entangled purification.”