9,662 research outputs found
Cost of quantum entanglement simplified
Quantum entanglement is a key physical resource in quantum information
processing that allows for performing basic quantum tasks such as teleportation
and quantum key distribution, which are impossible in the classical world. Ever
since the rise of quantum information theory, it has been an open problem to
quantify entanglement in an information-theoretically meaningful way. In
particular, every previously defined entanglement measure bearing a precise
information-theoretic meaning is not known to be efficiently computable, or if
it is efficiently computable, then it is not known to have a precise
information-theoretic meaning. In this Letter, we meet this challenge by
introducing an entanglement measure that has a precise information-theoretic
meaning as the exact cost required to prepare an entangled state when two
distant parties are allowed to perform quantum operations that completely
preserve the positivity of the partial transpose. Additionally, this
entanglement measure is efficiently computable by means of a semidefinite
program, and it bears a number of useful properties such as additivity and
faithfulness. Our results bring key insights into the fundamental entanglement
structure of arbitrary quantum states, and they can be used directly to assess
and quantify the entanglement produced in quantum-physical experiments.Comment: 7 pages of main text, 20 pages of supplementary material, companion
paper to arXiv:1809.0959
Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes
If entanglement is available, the error-correcting ability of quantum codes
can be increased. We show how to optimize the minimum distance of an
entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding
ebits to a standard quantum error-correcting code, over different encoding
operators. By this encoding optimization procedure, we found several new EAQEC
codes, including a family of [[n, 1, n; n-1]] EAQEC codes for n odd and code
parameters [[7, 1, 5; 2]], [[7, 1, 5; 3]], [[9, 1, 7; 4]], [[9, 1, 7; 5]],
which saturate the quantum singleton bound for EAQEC codes. A random search
algorithm for the encoding optimization procedure is also proposed.Comment: 39 pages, 10 table
The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes
Quantum error-correcting codes are used to protect quantum information from
decoherence. A raw state is mapped, by an encoding circuit, to a codeword so
that the most likely quantum errors from a noisy quantum channel can be removed
after a decoding process.
A good encoding circuit should have some desired features, such as low depth,
few gates, and so on. In this paper, we show how to practically implement an
encoding circuit of gate complexity for an
quantum stabilizer code with the help of pairs of maximally-entangled
states. For the special case of an stabilizer code with , the
encoding complexity is , which is previously known to be
. For this suggests that the benefits from shared
entanglement come at an additional cost of encoding complexity.
Finally we discuss decoding of entanglement-assisted quantum stabilizer codes
and extend previously known computational hardness results on decoding quantum
stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information
Theory (ISIT2019
Aspects of generic entanglement
We study entanglement and other correlation properties of random states in
high-dimensional bipartite systems. These correlations are quantified by
parameters that are subject to the "concentration of measure" phenomenon,
meaning that on a large-probability set these parameters are close to their
expectation. For the entropy of entanglement, this has the counterintuitive
consequence that there exist large subspaces in which all pure states are close
to maximally entangled. This, in turn, implies the existence of mixed states
with entanglement of formation near that of a maximally entangled state, but
with negligible quantum mutual information and, therefore, negligible
distillable entanglement, secret key, and common randomness. It also implies a
very strong locking effect for the entanglement of formation: its value can
jump from maximal to near zero by tracing over a number of qubits negligible
compared to the size of total system. Furthermore, such properties are generic.
Similar phenomena are observed for random multiparty states, leading us to
speculate on the possibility that the theory of entanglement is much simplified
when restricted to asymptotically generic states. Further consequences of our
results include a complete derandomization of the protocol for universal
superdense coding of quantum states.Comment: 22 pages, 1 figure, 1 tabl
Quantum communication cost of preparing multipartite entanglement
We study the preparation and distribution of high-fidelity multi-party
entangled states via noisy channels and operations. In the particular case of
GHZ and cluster states, we study different strategies using bipartite or
multipartite purification protocols. The most efficient strategy depends on the
target fidelity one wishes to achieve and on the quality of transmission
channel and local operations. We show the existence of a crossing point beyond
which the strategy making use of the purification of the state as a whole is
more efficient than a strategy in which pairs are purified before they are
connected to the final state. We also study the efficiency of intermediate
strategies, including sequences of purification and connection. We show that a
multipartite strategy is to be used if one wishes to achieve high fidelity,
whereas a bipartite strategy gives a better yield for low target fidelity.Comment: 21 pages, 17 figures; accepted for publication in Phys. Rev. A; v2:
corrections in figure
On the irreversibility of entanglement distillation
We investigate the irreversibility of entanglement distillation for a
symmetric d-1 parameter family of mixed bipartite quantum states acting on
Hilbert spaces of arbitrary dimension d x d. We prove that in this family the
entanglement cost is generically strictly larger than the distillable
entanglement, such that the set of states for which the distillation process is
asymptotically reversible is of measure zero. This remains true even if the
distillation process is catalytically assisted by pure state entanglement and
every operation is allowed, which preserves the positivity of the partial
transpose. It is shown, that reversibility occurs only in cases where the state
is quasi-pure in the sense that all its pure state entanglement can be revealed
by a simple operation on a single copy. The reversible cases are shown to be
completely characterized by minimal uncertainty vectors for entropic
uncertainty relations.Comment: 5 pages, revtex
Instantaneous nonlocal quantum computation and circuit depth reduction
Instantaneous two-party quantum computation is a computation process with
bipartite input and output, in which there are initial shared entanglement, and
the nonlocal interactions are limited to simultaneous classical communication
in both directions. It is almost equivalent to the problem of instantaneous
measurements, and is related to some topics in quantum foundations and
position-based quantum cryptography. In the first part of this work, we show
that a particular simplified subprocedure, known as a garden-hose gadget,
cannot significantly reduce the entanglement cost in instantaneous two-party
quantum computation. In the second part, we show that any unitary circuit
consisting of layers of Clifford gates and T gates can be implemented using a
circuit with measurements (or a unitary circuit) of depth proportional to the
T-depth of the original circuit. This result has some similarity with and also
some difference from a result in measurement-based quantum computation. It is
of limited use since interesting quantum algorithms often require a high ratio
of T gates, but still we discuss its extensions and applications.Comment: 6 pages. Revised Sec. 3 and the last part of Sec.
- …