996 research outputs found
Confusability graphs for symmetric sets of quantum states
For a set of quantum states generated by the action of a group, we consider
the graph obtained by considering two group elements adjacent whenever the
corresponding states are non-orthogonal. We analyze the structure of the
connected components of the graph and show two applications to the optimal
estimation of an unknown group action and to the search for decoherence free
subspaces of quantum channels with symmetry.Comment: 7 pages, no figures, contribution to the Proceedings of the XXIX
International Colloquium on Group-Theoretical Methods in Physics, August
22-26, Chern Institute of Mathematics, Tianjin, Chin
Optimal quantum operations at zero energy cost
Quantum technologies are developing powerful tools to generate and manipulate
coherent superpositions of different energy levels. Envisaging a new generation
of energy-efficient quantum devices, here we explore how coherence can be
manipulated without exchanging energy with the surrounding environment. We
start from the task of converting a coherent superposition of energy
eigenstates into another. We identify the optimal energy-preserving operations,
both in the deterministic and in the probabilistic scenario. We then design a
recursive protocol, wherein a branching sequence of energy-preserving filters
increases the probability of success while reaching maximum fidelity at each
iteration. Building on the recursive protocol, we construct efficient
approximations of the optimal fidelity-probability trade-off, by taking
coherent superpositions of the different branches generated by probabilistic
filtering. The benefits of this construction are illustrated in applications to
quantum metrology, quantum cloning, coherent state amplification, and
ancilla-driven computation. Finally, we extend our results to transitions where
the input state is generally mixed and we apply our findings to the task of
purifying quantum coherence.Comment: 35 pages, 10 figures; published versio
Efficient Quantum Compression for Ensembles of Identically Prepared Mixed States
We present one-shot compression protocols that optimally encode ensembles of
identically prepared mixed states into qubits. In contrast to
the case of pure-state ensembles, we find that the number of encoding qubits
drops down discontinuously as soon as a nonzero error is tolerated and the
spectrum of the states is known with sufficient precision. For qubit ensembles,
this feature leads to a 25% saving of memory space. Our compression protocols
can be implemented efficiently on a quantum computer.Comment: 5+19 pages, 2 figures. Published versio
Units of rotational information
Entanglement in angular momentum degrees of freedom is a precious resource
for quantum metrology and control. Here we study the conversions of this
resource, focusing on Bell pairs of spin-J particles, where one particle is
used to probe unknown rotations and the other particle is used as reference.
When a large number of pairs are given, we show that every rotated spin-J Bell
state can be reversibly converted into an equivalent number of rotated spin
one-half Bell states, at a rate determined by the quantum Fisher information.
This result provides the foundation for the definition of an elementary unit of
information about rotations in space, which we call the Cartesian refbit. In
the finite copy scenario, we design machines that approximately break down Bell
states of higher spins into Cartesian refbits, as well as machines that
approximately implement the inverse process. In addition, we establish a
quantitative link between the conversion of Bell states and the simulation of
unitary gates, showing that the fidelity of probabilistic state conversion
provides upper and lower bounds on the fidelity of deterministic gate
simulation. The result holds not only for rotation gates, but also to all sets
of gates that form finite-dimensional representations of compact groups. For
rotation gates, we show how rotations on a system of given spin can simulate
rotations on a system of different spin.Comment: 25 pages + appendix, 7 figures, new results adde
Quantum Metrology with Indefinite Causal Order
We address the study of quantum metrology enhanced by indefinite causal
order, demonstrating a quadratic advantage in the estimation of the product of
two average displacements in a continuous variable system. We prove that no
setup where the displacements are probed in a fixed order can have
root-mean-square error vanishing faster than the Heisenberg limit 1/N, where N
is the number of displacements contributing to the average. In stark contrast,
we show that a setup that probes the displacements in a superposition of two
alternative orders yields a root-mean-square error vanishing with
super-Heisenberg scaling 1/N^2. This result opens up the study of new
measurement setups where quantum processes are probed in an indefinite order,
and suggests enhanced tests of the canonical commutation relations, with
potential applications to quantum gravity.Comment: 11 pages, 3 figure
Quantum Stopwatch: How To Store Time in a Quantum Memory
Quantum mechanics imposes a fundamental tradeoff between the accuracy of time
measurements and the size of the systems used as clocks. When the measurements
of different time intervals are combined, the errors due to the finite clock
size accumulate, resulting in an overall inaccuracy that grows with the
complexity of the setup. Here we introduce a method that in principle eludes
the accumulation of errors by coherently transferring information from a
quantum clock to a quantum memory of the smallest possible size. Our method
could be used to measure the total duration of a sequence of events with
enhanced accuracy, and to reduce the amount of quantum communication needed to
stabilize clocks in a quantum network.Comment: 10 + 5 pages, 3 figure
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