22,223 research outputs found
A Compressed Classical Description of Quantum States
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an n-qubit state psi consists of its inner products with O(sqrt{2^n}) stabilizer states. A quantum state initially specified by its 2^n entries in the computational basis can be compressed to this form in time O(2^n poly(n)), and, subsequently, the compressed description can be used to additively approximate the expectation value of an arbitrary observable. Our compression scheme directly gives a new protocol for the vector in subspace problem with randomized one-way communication complexity that matches (up to polylogarithmic factors) the optimal upper bound, due to Raz. We obtain an exponential improvement over Raz\u27s protocol in terms of computational efficiency
Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability
Game-playing proofs constitute a powerful framework for non-quantum
cryptographic security arguments, most notably applied in the context of
indifferentiability. An essential ingredient in such proofs is lazy sampling of
random primitives. We develop a quantum game-playing proof framework by
generalizing two recently developed proof techniques. First, we describe how
Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy
sampling of a class of non-uniform function distributions. Second, we observe
how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied to
compressed oracles, providing a quantum counterpart to the fundamental lemma of
game-playing. Subsequently, we use our game-playing framework to prove quantum
indifferentiability of the sponge construction, assuming a random internal
function
Energy Requirements for Quantum Data Compression and 1-1 Coding
By looking at quantum data compression in the second quantisation, we present
a new model for the efficient generation and use of variable length codes. In
this picture lossless data compression can be seen as the {\em minimum energy}
required to faithfully represent or transmit classical information contained
within a quantum state.
In order to represent information we create quanta in some predefined modes
(i.e. frequencies) prepared in one of two possible internal states (the
information carrying degrees of freedom). Data compression is now seen as the
selective annihilation of these quanta, the energy of whom is effectively
dissipated into the environment. As any increase in the energy of the
environment is intricately linked to any information loss and is subject to
Landauer's erasure principle, we use this principle to distinguish lossless and
lossy schemes and to suggest bounds on the efficiency of our lossless
compression protocol.
In line with the work of Bostr\"{o}m and Felbinger \cite{bostroem}, we also
show that when using variable length codes the classical notions of prefix or
uniquely decipherable codes are unnecessarily restrictive given the structure
of quantum mechanics and that a 1-1 mapping is sufficient. In the absence of
this restraint we translate existing classical results on 1-1 coding to the
quantum domain to derive a new upper bound on the compression of quantum
information. Finally we present a simple quantum circuit to implement our
scheme.Comment: 10 pages, 5 figure
Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix
We clarify different definitions of the density matrix by proposing the use
of different names, the full density matrix for a single-closed quantum system,
the compressed density matrix for the averaged single molecule state from an
ensemble of molecules, and the reduced density matrix for a part of an
entangled quantum system, respectively. We show that ensembles with the same
compressed density matrix can be physically distinguished by observing
fluctuations of various observables. This is in contrast to a general belief
that ensembles with the same compressed density matrix are identical. Explicit
expression for the fluctuation of an observable in a specified ensemble is
given. We have discussed the nature of nuclear magnetic resonance quantum
computing. We show that the conclusion that there is no quantum entanglement in
the current nuclear magnetic resonance quantum computing experiment is based on
the unjustified belief that ensembles having the same compressed density matrix
are identical physically. Related issues in quantum communication are also
discussed.Comment: 26 pages. To appear in Foundations of Physics, 36 (8), 200
Expansion and evaporation of hot nuclei: Comparison between semi-classical and quantal mean-field approaches
We present a general discussion of the mean field dynamics of finite nuclei
prepared under extreme conditions of temperature and pressure. We compare the
prediction of semi-classical approximation with complete quantum simulations.
Many features of the dynamics are carefully studied such as the collective
expansion, the evaporation process, the different time-scale... This study
points out many quantitative differences between quantum and semi-classical
approaches. Part of the differences are related to numerical features inherent
in semi-classical simulations but most of them are a direct consequence of the
non treatment of nuclei as quantal objects. In particular, we show that because
of a too strong damping in semi-classical approaches the expansion of hot
nuclei is quenched and the speed of the collective motion reduced.Comment: 41 pages including 14 figure
Randomness in Classical Mechanics and Quantum Mechanics
The Copenhagen interpretation of quantum mechanics assumes the existence of
the classical deterministic Newtonian world. We argue that in fact the Newton
determinism in classical world does not hold and in classical mechanics there
is fundamental and irreducible randomness. The classical Newtonian trajectory
does not have a direct physical meaning since arbitrary real numbers are not
observable. There are classical uncertainty relations, i.e. the uncertainty
(errors of observation) in the determination of coordinate and momentum is
always positive (non zero).
A "functional" formulation of classical mechanics was suggested. The
fundamental equation of the microscopic dynamics in the functional approach is
not the Newton equation but the Liouville equation for the distribution
function of the single particle. Solutions of the Liouville equation have the
property of delocalization which accounts for irreversibility. The Newton
equation in this approach appears as an approximate equation describing the
dynamics of the average values of the position and momenta for not too long
time intervals. Corrections to the Newton trajectories are computed. An
interpretation of quantum mechanics is attempted in which both classical and
quantum mechanics contain fundamental randomness. Instead of an ensemble of
events one introduces an ensemble of observers.Comment: 12 pages, Late
Achieving minimum-error discrimination of an arbitrary set of laser-light pulses
Laser light is widely used for communication and sensing applications, so the
optimal discrimination of coherent states--the quantum states of light emitted
by a laser--has immense practical importance. However, quantum mechanics
imposes a fundamental limit on how well different coher- ent states can be
distinguished, even with perfect detectors, and limits such discrimination to
have a finite minimum probability of error. While conventional optical
receivers lead to error rates well above this fundamental limit, Dolinar found
an explicit receiver design involving optical feedback and photon counting that
can achieve the minimum probability of error for discriminating any two given
coherent states. The generalization of this construction to larger sets of
coherent states has proven to be challenging, evidencing that there may be a
limitation inherent to a linear-optics-based adaptive measurement strategy. In
this Letter, we show how to achieve optimal discrimination of any set of
coherent states using a resource-efficient quantum computer. Our construction
leverages a recent result on discriminating multi-copy quantum hypotheses
(arXiv:1201.6625) and properties of coherent states. Furthermore, our
construction is reusable, composable, and applicable to designing
quantum-limited processing of coherent-state signals to optimize any metric of
choice. As illustrative examples, we analyze the performance of discriminating
a ternary alphabet, and show how the quantum circuit of a receiver designed to
discriminate a binary alphabet can be reused in discriminating multimode
hypotheses. Finally, we show our result can be used to achieve the quantum
limit on the rate of classical information transmission on a lossy optical
channel, which is known to exceed the Shannon rate of all conventional optical
receivers.Comment: 9 pages, 2 figures; v2 Minor correction
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