421 research outputs found
Reversible simulation of bipartite product Hamiltonians
Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.Comment: 10 page
Adiabatic Quantum State Generation and Statistical Zero Knowledge
The design of new quantum algorithms has proven to be an extremely difficult
task. This paper considers a different approach to the problem, by studying the
problem of 'quantum state generation'. This approach provides intriguing links
between many different areas: quantum computation, adiabatic evolution,
analysis of spectral gaps and groundstates of Hamiltonians, rapidly mixing
Markov chains, the complexity class statistical zero knowledge, quantum random
walks, and more.
We first show that many natural candidates for quantum algorithms can be cast
as a state generation problem. We define a paradigm for state generation,
called 'adiabatic state generation' and develop tools for adiabatic state
generation which include methods for implementing very general Hamiltonians and
ways to guarantee non negligible spectral gaps. We use our tools to prove that
adiabatic state generation is equivalent to state generation in the standard
quantum computing model, and finally we show how to apply our techniques to
generate interesting superpositions related to Markov chains.Comment: 35 pages, two figure
Optimal Entanglement Generation from Quantum Operations
We consider how much entanglement can be produced by a non-local two-qubit
unitary operation, - the entangling capacity of . For a single
application of , with no ancillas, we find the entangling capacity and
show that it generally helps to act with on an entangled state.
Allowing ancillas, we present numerical results from which we can conclude,
quite generally, that allowing initial entanglement typically increases the
optimal capacity in this case as well. Next, we show that allowing collective
processing does not increase the entangling capacity if initial entanglement is
allowed.Comment: v1.0 15 pages, 3 figures, written in revtex4. v2.0 References
updated. Submitted to Phys. Rev. A v3.0 16 pages, 4 figures. Expanded
explanation in section 3A, figures corrected and made clearer. Definition of
entangling capacity in section 4 made explicit. Other minor typos correcte
Implementation of multipartite unitary operations with limited resources
A general method for implementing weakly entangling multipartite unitary
operations using a small amount of entanglement and classical communication is
presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method
requires less entanglement than previously known methods. In addition,
compression of multiple operations is applied to reduce the average
communication required.Comment: 7 pages, 4 figures, comments welcom
Upper bounds on entangling rates of bipartite Hamiltonians
We discuss upper bounds on the rate at which unitary evolution governed by a
non-local Hamiltonian can generate entanglement in a bipartite system. Given a
bipartite Hamiltonian H coupling two finite dimensional particles A and B, the
entangling rate is shown to be upper bounded by c*log(d)*norm(H), where d is
the smallest dimension of the interacting particles, norm(H) is the operator
norm of H, and c is a constant close to 1. Under certain restrictions on the
initial state we prove analogous upper bound for the ancilla-assisted
entangling rate with a constant c that does not depend upon dimensions of local
ancillas. The restriction is that the initial state has at most two distinct
Schmidt coefficients (each coefficient may have arbitrarily large
multiplicity). Our proof is based on analysis of a mixing rate -- a functional
measuring how fast entropy can be produced if one mixes a time-independent
state with a state evolving unitarily.Comment: 14 pages, 4 figure
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