Herbert J. Bernstein

Concentrating partial entanglement by local operations

If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement. \textcopyright{} 1996 The American Physical Society.

Finding a better-than-classical quantum AND/OR algorithm using genetic programming

This paper documents the discovery of a new, better-than-classical quantum algorithm for the depth-two AND/OR tree problem. We describe the genetic programming system that was constructed specifically for this work, the quantum computer simulator that is used to evaluate the fitness of evolving quantum algorithms, and the newly discovered algorithm.

Quantum circuits for OR and AND of ORs

We give the first quantum circuit for computing f( 0)OR f( 1)more reliably than is classically possible with a single evaluation of the function. OR therefore joins XOR (i.e. parity, f( 0)f( 1)) to give the full set of logical connectives (up to relabelling of inputs and outputs) for which there is quantum speedup.

Superdense teleportation using hyperentangled photons

Transmitting quantum information between two remote parties is a requirement for many quantum applications; however, direct transmission of states is often impossible because of noise and loss in the communication channel. Entanglement-enhanced state communication can be used to avoid this issue, but current techniques require extensive experimental resources to transmit large quantum states deterministically. To reduce these resource requirements, we use photon pairs hyperentangled in polarization and orbital angular momentum to implement superdense teleportation, which can communicate a specific class of single-photon ququarts. We achieve an average fidelity of 87.0(1)%, almost twice the classical limit of 44% with reduced experimental resources than traditional techniques. We conclude by discussing the information content of this constrained set of states and demonstrate that this set has an exponentially larger state space volume than the lower-dimensional general states with the same number of state parameters.

Information Transfer with Two-state Two-particle Quantum Systems

Abstract Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any N-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode log23 = 1·57 bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon,...

Exact spin rotation by precession during neutron interferometry

Abstract Time dependent magnetic fields can be used to produce exact rotations of spin wavefunctions. This avoids the inherent approximations encountered in experiments performed with static fields to demonstrate the effect of 2π-rotations on fermions. Two of the experiments proposed explicitly will use forthcoming interferometers for ultra cold neutrons.

Must quantum theory assume unrestricted superposition

A conjecture that the (n −1)2 independent moduli and (2n −1) unphysical phases completely specify all n‐dimensional unitary matrices is shown to be true in two and three dimensions, but false in four or more. The implications for quantum theory are discussed.

Superdense teleportation and quantum key distribution for space applications

The transfer of quantum information over long distances has long been a goal of quantum information science and is required for many important quantum communication and computing protocols. When these channels are lossy and noisy, it is often impossible to directly transmit quantum states between two distant parties. We use a new technique called superdense teleportation to communicate quantum information deterministically with greatly reduced resources, simplified measurements, and decreased classical communication cost. These advantages make this technique ideal for communicating quantum information for space applications. We are currently implementing an superdense teleportation lab demonstration, using photons hyperentangled in polarization and temporal mode to communicate a special set of two-qubit, single-photon states between two remote parties. A slight modification of the system readily allows it to be used to implement quantum cryptography as well. We investigate the possibility of implementation from an Earths orbit to ground. We will discuss our current experimental progress and the design challenges facing a practical demonstration of satellite-to-Earth SDT.

Superdense teleportation for space applications

We report the implementation of a novel entanglement-enabled quantum state communication protocol, known as SuperDense Teleportation, using photons hyperentangled in polarization and orbital angular momentum. We used these techniques to transmit unimodular ququart states between distant parties with an averaged fidelity of 86.2±3%; almost twice the classical limit of 44%. We also propose a method to use SuperDense Teleportation to communicate quantum states from a space platform, such as the International Space Station, to a terrestrial optical telescope. We evaluate several configurations and investigate the challenges arising from the movement of the space station with respect to the ground.

Neutron spin-pendellösung resonance

Abstract A novel resonant enhancement of the spin-orbit scattering of thermal neutrons in a perfect crystal is predicted. The effect occurs when the Larmor precession distance for the neutron in an externally applied magnetic field coincides with the pendellosung distance in the crystal. The potential is described, the wave functions are derived, and an experiment is proposed.