202 research outputs found
Deterministic Quantum State Transformations
We derive a necessary condition for the existence of a completely-positive,
linear, trace-preserving map which deterministically transforms one finite set
of pure quantum states into another. This condition is also sufficient for
linearly-independent initial states. We also examine the issue of quantum
coherence, that is, when such operations maintain the purity of superpositions.
If, in any deterministic transformation from one linearly-independent set to
another, even a single, complete superposition of the initial states maintains
its purity, the initial and final states are related by a unitary
transformation.Comment: Minor cosmetic change
Optimum Unambiguous Discrimination Between Linearly Independent Symmetric States
The quantum formalism permits one to discriminate sometimes between any set
of linearly-independent pure states with certainty. We obtain the maximum
probability with which a set of equally-likely, symmetric, linearly-independent
states can be discriminated. The form of this bound is examined for symmetric
coherent states of a harmonic oscillator or field mode.Comment: 9 pages, 2 eps figures, submitted to Physics Letters
General Strategies for Discrimination of Quantum States
We derive general discrimination of quantum states chosen from a certain set,
given initial copies of each state, and obtain the matrix inequality, which
describe the bound between the maximum probability of correctly determining and
that of error. The former works are special cases of our results.Comment: 8 Pages, No Figure, REVTe
Unambiguous Discrimination Between Linearly Dependent States with Multiple Copies
A set of quantum states can be unambiguously discriminated if and only if
they are linearly independent. However, for a linearly dependent set, if C
copies of the state are available, then the resulting C particle states may
form a linearly independent set, and be amenable to unambiguous discrimination.
We obtain necessary and sufficient conditions for the possibility of
unambiguous discrimination between N states given that C copies are available
and that the single copies span a D dimensional space. These conditions are
found to be identical for qubits. We then examine in detail the linearly
dependent trine ensemble. The set of C>1 copies of each state is a set of
linearly independent lifted trine states. The maximum unambiguous
discrimination probability is evaluated for all C>1 with equal a priori
probabilities.Comment: 12 Pages RevTeX 4, 1 EPS figur
Distributed implementation of standard oracle operators
The standard oracle operator corresponding to a function f is a unitary
operator that computes this function coherently, i.e. it maintains
superpositions. This operator acts on a bipartite system, where the subsystems
are the input and output registers. In distributed quantum computation, these
subsystems may be spatially separated, in which case we will be interested in
its classical and entangling capacities. For an arbitrary function f, we show
that the unidirectional classical and entangling capacities of this operator
are log_{2}(n_{f}) bits/ebits, where n_{f} is the number of different values
this function can take. An optimal procedure for bidirectional classical
communication with a standard oracle operator corresponding to a permutation on
Z_{M} is given. The bidirectional classical capacity of such an operator is
found to be 2log_{2}(M) bits. The proofs of these capacities are facilitated by
an optimal distributed protocol for the implementation of an arbitrary standard
oracle operator.Comment: 4.4 pages, Revtex 4. Submitted to Physical Review Letter
Unambiguous Discrimination Between Linearly-Independent Quantum States
The theory of generalised measurements is used to examine the problem of
discriminating unambiguously between non-orthogonal pure quantum states.
Measurements of this type never give erroneous results, although, in general,
there will be a non-zero probability of a result being inconclusive. It is
shown that only linearly-independent states can be unambiguously discriminated.
In addition to examining the general properties of such measurements, we
discuss their application to entanglement concentration
Optimal phase estimation and square root measurement
We present an optimal strategy having finite outcomes for estimating a single
parameter of the displacement operator on an arbitrary finite dimensional
system using a finite number of identical samples. Assuming the uniform {\it a
priori} distribution for the displacement parameter, an optimal strategy can be
constructed by making the {\it square root measurement} based on uniformly
distributed sample points. This type of measurement automatically ensures the
global maximality of the figure of merit, that is, the so called average score
or fidelity. Quantum circuit implementations for the optimal strategies are
provided in the case of a two dimensional system.Comment: Latex, 5 figure
- …