1,634 research outputs found
Information gain versus state disturbance for a single qubit
The trade-off between the information gain and the state disturbance is
derived for quantum operations on a single qubit prepared in a uniformly
distributed pure state. The derivation is valid for a class of measures
quantifying the state disturbance and the information gain which satisfy
certain invariance conditions. This class includes in particular the Shannon
entropy versus the operation fidelity. The central role in the derivation is
played by efficient quantum operations, which leave the system in a pure output
state for any measurement outcome. It is pointed out that the optimality of
efficient quantum operations among those inducing a given operator-valued
measure is related to Davies' characterization of convex invariant functions on
hermitian operators.Comment: 17 pages, LaTeX, osid.sty. Substantially expanded and generalize
The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
We represent generalized density matrices of a -complex dimensional
quantum system as a subcone of a real pointed cone of revolution in
, or indeed a Minkowskian cone in .
Generalized pure states correspond to certain future-directed light-like
vectors of . This extension of the Generalized Bloch
Sphere enables us to cater for non-trace-preserving quantum operations, and in
particluar to view the per-outcome effects of generalized measurements. We show
that these consist of the product of an orthogonal transform about the axis of
the cone of revolution and a positive real linear transform. We give detailed
formulae for the one qubit case and express the post-measurement states in
terms of the initial state vectors and measurement vectors. We apply these
results in order to find the information gain versus disturbance tradeoff in
the case of two equiprobable pure states. Thus we recover Fuchs and Peres'
formula in an elegant manner.Comment: 11 pages, revtex, v3: some typos correcte
Separating the classical and quantum information via quantum cloning
An application of quantum cloning to optimally interface a quantum system
with a classical observer is presented, in particular we describe a procedure
to perform a minimal disturbance measurement on a single qubit by adopting a
1->2 cloning machine followed by a generalized measurement on a single clone
and the anti-clone or on the two clones. Such scheme has been applied to
enhance the transmission fidelity over a lossy quantum channel.Comment: 4 pages, 2figure
Quantum copying: Fundamental inequalities
How well one can copy an arbitrary qubit? To answer this question we consider
two arbitrary vectors in a two-dimensional state space and an abstract copying
transformation which will copy these two vectors. If the vectors are
orthogonal, then perfect copies can be made. If they are not, then errors will
be introduced. The size of the error depends on the inner product of the two
original vectors. We derive a lower bound for the amount of noise induced by
quantum copying. We examine both copying transformations which produce one copy
and transformations which produce many, and show that the quality of each copy
decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.
In defense of the epistemic view of quantum states: a toy theory
We present a toy theory that is based on a simple principle: the number of
questions about the physical state of a system that are answered must always be
equal to the number that are unanswered in a state of maximal knowledge. A wide
variety of quantum phenomena are found to have analogues within this toy
theory. Such phenomena include: the noncommutativity of measurements,
interference, the multiplicity of convex decompositions of a mixed state, the
impossibility of discriminating nonorthogonal states, the impossibility of a
universal state inverter, the distinction between bi-partite and tri-partite
entanglement, the monogamy of pure entanglement, no cloning, no broadcasting,
remote steering, teleportation, dense coding, mutually unbiased bases, and many
others. The diversity and quality of these analogies is taken as evidence for
the view that quantum states are states of incomplete knowledge rather than
states of reality. A consideration of the phenomena that the toy theory fails
to reproduce, notably, violations of Bell inequalities and the existence of a
Kochen-Specker theorem, provides clues for how to proceed with this research
program.Comment: 32 pages, REVTEX, based on a talk given at the Rob Clifton Memorial
Conference, College Park, May 2003; v2: minor modifications throughout,
updated reference
Qubit state tomography in superconducting circuit via weak measurements
The standard method of "measuring" quantum wavefunction is the technique of
{\it indirect} quantum state tomography. Owing to conceptual novelty and
possible advantages, an alternative {\it direct} scheme was proposed and
demonstrated recently in quantum optics system. In this work we present a study
on the direct scheme of measuring qubit state in the circuit QED system, based
on weak measurement and weak value concepts. To be applied to generic parameter
conditions, our formulation and analysis are carried out for finite strength
weak measurement, and in particular beyond the bad-cavity and weak-response
limits. The proposed study is accessible to the present state-of-the-art
circuit-QED experiments.Comment: 7 pages,5figure
Recycling of quantum information: Multiple observations of quantum systems
Given a finite number of copies of an unknown qubit state that have already
been measured optimally, can one still extract any information about the
original unknown state? We give a positive answer to this question and quantify
the information obtainable by a given observer as a function of the number of
copies in the ensemble, and of the number of independent observers that, one
after the other, have independently measured the same ensemble of qubits before
him. The optimality of the protocol is proven and extensions to other states
and encodings are also studied. According to the general lore, the state after
a measurement has no information about the state before the measurement. Our
results manifestly show that this statement has to be taken with a grain of
salt, specially in situations where the quantum states encode confidential
information.Comment: 4 page
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