509 research outputs found
Entanglement cost and quantum channel simulation
This paper proposes a revised definition for the entanglement cost of a
quantum channel . In particular, it is defined here to be the
smallest rate at which entanglement is required, in addition to free classical
communication, in order to simulate calls to , such that the
most general discriminator cannot distinguish the calls to
from the simulation. The most general discriminator is one who tests the
channels in a sequential manner, one after the other, and this discriminator is
known as a quantum tester [Chiribella et al., Phys. Rev. Lett., 101, 060401
(2008)] or one who is implementing a quantum co-strategy [Gutoski et al., Symp.
Th. Comp., 565 (2007)]. As such, the proposed revised definition of
entanglement cost of a quantum channel leads to a rate that cannot be smaller
than the previous notion of a channel's entanglement cost [Berta et al., IEEE
Trans. Inf. Theory, 59, 6779 (2013)], in which the discriminator is limited to
distinguishing parallel uses of the channel from the simulation. Under this
revised notion, I prove that the entanglement cost of certain
teleportation-simulable channels is equal to the entanglement cost of their
underlying resource states. Then I find single-letter formulas for the
entanglement cost of some fundamental channel models, including dephasing,
erasure, three-dimensional Werner--Holevo channels, epolarizing channels
(complements of depolarizing channels), as well as single-mode pure-loss and
pure-amplifier bosonic Gaussian channels. These examples demonstrate that the
resource theory of entanglement for quantum channels is not reversible.
Finally, I discuss how to generalize the basic notions to arbitrary resource
theories.Comment: 28 pages, 7 figure
Entanglement consumption of instantaneous nonlocal quantum measurements
Relativistic causality has dramatic consequences on the measurability of
nonlocal variables and poses the fundamental question of whether it is
physically meaningful to speak about the value of nonlocal variables at a
particular time. Recent work has shown that by weakening the role of the
measurement in preparing eigenstates of the variable it is in fact possible to
measure all nonlocal observables instantaneously by exploiting entanglement.
However, for these measurement schemes to succeed with certainty an infinite
amount of entanglement must be distributed initially and all this entanglement
is necessarily consumed. In this work we sharpen the characterisation of
instantaneous nonlocal measurements by explicitly devising schemes in which
only a finite amount of the initially distributed entanglement is ever
utilised. This enables us to determine an upper bound to the average
consumption for the most general cases of nonlocal measurements. This includes
the tasks of state verification, where the measurement verifies if the system
is in a given state, and verification measurements of a general set of
eigenstates of an observable. Despite its finiteness the growth of entanglement
consumption is found to display an extremely unfavourable exponential of an
exponential scaling with either the number of qubits needed to contain the
Schmidt rank of the target state or total number of qubits in the system for an
operator measurement. This scaling is seen to be a consequence of the
combination of the generic exponential scaling of unitary decompositions
combined with the highly recursive structure of our scheme required to overcome
the no-signalling constraint of relativistic causality.Comment: 32 pages and 14 figures. Updated to published versio
Entanglement in continuous variable systems: Recent advances and current perspectives
We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J.
Phys. A, Special Issue on Quantum Information, Communication, Computation and
Cryptography (v3: few typos corrected
Asymptotic performance of port-based teleportation
Quantum teleportation is one of the fundamental building blocks of quantum
Shannon theory. While ordinary teleportation is simple and efficient,
port-based teleportation (PBT) enables applications such as universal
programmable quantum processors, instantaneous non-local quantum computation
and attacks on position-based quantum cryptography. In this work, we determine
the fundamental limit on the performance of PBT: for arbitrary fixed input
dimension and a large number of ports, the error of the optimal protocol is
proportional to the inverse square of . We prove this by deriving an
achievability bound, obtained by relating the corresponding optimization
problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered
simplex. We also give an improved converse bound of matching order in the
number of ports. In addition, we determine the leading-order asymptotics of PBT
variants defined in terms of maximally entangled resource states. The proofs of
these results rely on connecting recently-derived representation-theoretic
formulas to random matrix theory. Along the way, we refine a convergence result
for the fluctuations of the Schur-Weyl distribution by Johansson, which might
be of independent interest.Comment: 68 pages, 4 figures; comments welcome! v2: minor fixes, added plots
comparing asymptotic expansions to exact formulas, code available at
https://github.com/amsqi/port-base
Unitarity of black hole evaporation in final-state projection models
Almheiri et al. have emphasized that otherwise reasonable beliefs about black
hole evaporation are incompatible with the monogamy of quantum entanglement, a
general property of quantum mechanics. We investigate the final-state
projection model of black hole evaporation proposed by Horowitz and Maldacena,
pointing out that this model admits cloning of quantum states and polygamous
entanglement, allowing unitarity of the evaporation process to be reconciled
with smoothness of the black hole event horizon. Though the model seems to
require carefully tuned dynamics to ensure exact unitarity of the black hole
S-matrix, for a generic final-state boundary condition the deviations from
unitarity are exponentially small in the black hole entropy; furthermore
observers inside black holes need not detect any deviations from standard
quantum mechanics. Though measurements performed inside old black holes could
potentially produce causality-violating phenomena, the computational complexity
of decoding the Hawking radiation may render the causality violation
unobservable. Final-state projection models illustrate how inviolable
principles of standard quantum mechanics might be circumvented in a theory of
quantum gravity.Comment: (v3) 27 pages, 16 figures. Expanded discussion of measurements inside
black hole
Bipartite Entanglement in Continuous-Variable Cluster States
We present a study of the entanglement properties of Gaussian cluster states,
proposed as a universal resource for continuous-variable quantum computing. A
central aim is to compare mathematically-idealized cluster states defined using
quadrature eigenstates, which have infinite squeezing and cannot exist in
nature, with Gaussian approximations which are experimentally accessible.
Adopting widely-used definitions, we first review the key concepts, by
analysing a process of teleportation along a continuous-variable quantum wire
in the language of matrix product states. Next we consider the bipartite
entanglement properties of the wire, providing analytic results. We proceed to
grid cluster states, which are universal for the qubit case. To extend our
analysis of the bipartite entanglement, we adopt the entropic-entanglement
width, a specialized entanglement measure introduced recently by Van den Nest M
et al., Phys. Rev. Lett. 97 150504 (2006), adapting their definition to the
continuous-variable context. Finally we add the effects of photonic loss,
extending our arguments to mixed states. Cumulatively our results point to key
differences in the properties of idealized and Gaussian cluster states. Even
modest loss rates are found to strongly limit the amount of entanglement. We
discuss the implications for the potential of continuous-variable analogues of
measurement-based quantum computation.Comment: 22 page
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