438 research outputs found
A simple operational interpretation of the fidelity
This note presents a corollary to Uhlmann's theorem which provides a simple
operational interpretation for the fidelity of mixed states.Comment: 1 pag
Distinguishability of States and von Neumann Entropy
Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with
prior probabilities p_j respectively. We show that it is possible to increase
all of the pairwise overlaps || i.e. make each constituent pair
of the states more parallel (while keeping the prior probabilities the same),
in such a way that the von Neumann entropy S is increased, and dually, make all
pairs more orthogonal while decreasing S. We show that this phenomenon cannot
occur for ensembles in two dimensions but that it is a feature of almost all
ensembles of three states in three dimensions. It is known that the von Neumann
entropy characterises the classical and quantum information capacities of the
ensemble and we argue that information capacity in turn, is a manifestation of
the distinguishability of the signal states. Hence our result shows that the
notion of distinguishability within an ensemble is a global property that
cannot be reduced to considering distinguishability of each constituent pair of
states.Comment: 18 pages, Latex, 2 figure
On quantum coding for ensembles of mixed states
We consider the problem of optimal asymptotically faithful compression for
ensembles of mixed quantum states. Although the optimal rate is unknown, we
prove upper and lower bounds and describe a series of illustrative examples of
compression of mixed states. We also discuss a classical analogue of the
problem.Comment: 23 pages, LaTe
Mimicking Time Evolution within a Quantum Ground State: Ground-State Quantum Computation, Cloning, and Teleportation
Ground-state quantum computers mimic quantum mechanical time evolution within
the amplitudes of a time-independent quantum state. We explore the principles
that constrain this mimicking. A no-cloning argument is found to impose strong
restrictions. It is shown, however, that there is flexibility that can be
exploited using quantum teleportation methods to improve ground-state quantum
computer design.Comment: 10 pages, 7 figure
Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators
We propose a new strategy to physically implement a universal set of quantum
gates based on geometric phases accumulated in the nondegenerate eigenstates of
a designated invariant operator in a periodic physical system. The system is
driven to evolve in such a way that the dynamical phase shifts of the invariant
operator eigenstates are the same (or {\it mod} ) while the corresponding
geometric phases are nontrivial.
We illustrate how this strategy to work in a simple but typical NMR-type
qubit system.Comment: 4 page
Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance
The role of mixed state entanglement in liquid-state nuclear magnetic
resonance (NMR) quantum computation is not yet well-understood. In particular,
despite the success of quantum information processing with NMR, recent work has
shown that quantum states used in most of those experiments were not entangled.
This is because these states, derived by unitary transforms from the thermal
equilibrium state, were too close to the maximally mixed state. We are thus
motivated to determine whether a given NMR state is entanglable - that is, does
there exist a unitary transform that entangles the state? The boundary between
entanglable and nonentanglable thermal states is a function of the spin system
size and its temperature . We provide new bounds on the location of this
boundary using analytical and numerical methods; our tightest bound scales as
, giving a lower bound requiring at least proton
spins to realize an entanglable thermal state at typical laboratory NMR
magnetic fields. These bounds are tighter than known bounds on the
entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K
Lossless quantum data compression and variable-length coding
In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.Comment: 16 pages, 5 figure
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