arXiv subjects

Benni Reznik

Publications and source records attributed to Benni Reznik.

At least 37 records · Page 2Linked to original sources

arXiv2011

Structural unification of space and time correlations in quantum theory

We suggest a natural mapping between bipartite states and quantum evolutions of local states, which is a Jamiolkowski map. It is shown that spatial correlations of weak measurements in bipartite systems precisely coincide with temporal correlations of local systems. This mapping has several practical and conceptual implications on the correspondence between Bell and Leggett-Garg inequalities, the statistical properties of evolutions in large systems, temporal decoherence and computational gain, in evaluation of spatial correlations of large systems.

quant-ph↗

arXiv2011

Testing Bell inequalities with weak measurements

Quantum theory is inconsistent with any local hidden variable model as was first shown by Bell. To test Bell inequalities two separated observers extract correlations from a common ensemble of identical systems. Since quantum theory does not allow simultaneous measurements of noncommuting observables, on each system every party measures a single randomly chosen observable out of a given set. Here we suggest a different approach for testing Bell inequalities that is experimentally realizable by current methods. We show that Bell inequalities can be maximally violated even when all observables are measured on each member of the ensemble. This is possible by using weak measurements that produce small disturbance, at the expense of accuracy. However, our approach does not constitute an independent test of quantum nonlocality since the local hidden variables may correlate the noise of the measurement instruments. Nevertheless, by adding a randomly chosen precise measurement at the end of every cycle of weak measurements, the parties can verify that the hidden variables were not interfering with the noise, and thus validate the suggested test.

quant-ph↗

arXiv2010

How to derive quantum formalism from first principles?

Suggested a framework to derive the formalism of quantum theory based on the work of Navascues, Pironio and Acin [NJP 10, 073013] (NPA). Specifically, the entries in the Gamma matrices in NPA corrspond to sequential weak values, first analyzed by Mitchison, Popescu and Jozsa [PRA 76, 062105]. However, to obtain the sequential weak values post-selection to the initial state is required, for which we could not find sufficiently strong reason.

quant-ph↗

arXiv2010

Hawking Radiation from an Acoustic Black Hole on an Ion Ring

In this article we propose to simulate acoustic black holes with ions in rings. If the ions are rotating with a stationary and inhomogeneous velocity profile, regions can appear where the ion velocity exceeds the group velocity of the phonons. In these regions phonons are trapped like light in black holes, even though we have a discrete field theory and a nonlinear dispersion relation. We study the appearance of Hawking radiation in this setup and propose a scheme to detect it.

quant-ph↗

arXiv2009

Fundamental destruction of information and conservation laws

Theories which have fundamental information destruction or decoherence are motivated by the black hole information paradox where one appears to have pure states evolving into mixed states. However such theories have either violated conservation laws, or are highly non-local. Here, we show that the tension between conservation laws and locality can be circumvented by constructing a relational theory of information destruction. In terms of conservation laws, we derive a generalisation of Noether's theorem for general theories, and show that symmetries imply a strong restriction on the type of evolution permissable. With respect to locality, we distinguish violations of causality from the creation or destruction of space-like seperated correlations. We show that violations of causality need not occur in a relational framework, although one can have situations where correlations decay faster than one might otherwise expect or can be created over spatial distances. This creation or destruction of correlations cannot be used to signal superluminally, and thus no violation of causality occurs. We prove that theories with information destruction can be made time-symmetric, thus impossing no arrow of time.

hep-th↗

arXiv2008

Entanglement of Solitons in the Frenkel-Kontorova Model

We investigate entanglement of solitons in the continuum-limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particle-like behavior as they are characterized by localization of entanglement. The von-Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two solitons manifest long-range entanglement that decreases with the separation of the solitons more slowly than the universal decrease of the critical field. Interestingly, in the noncritical regime of the Frenkel-Kontorova model, entanglement can even increase with the separation of the solitons. We show that most of the entanglement of the so-called internal modes of the solitons is saturated by local degrees of freedom inside the core, and therefore we suggest using the internal modes as carriers of quantum information.

quant-ph↗

arXiv2008

Entanglement and the Speed of Evolution in Mixed States

Entanglement speeds up evolution of a pure bipartite spin state, in line with the time energy uncertainty. However if the state is mixed this is not necessarily the case. We provide a counter example and point to other factors affecting evolution in mixed states, including classical correlations and entropy.

quant-ph↗

arXiv2007

Is Communication Complexity Physical?

Recently, Brassard et. al. conjectured that the fact that the maximal possible correlations between two non-local parties are the quantum-mechanical ones is linked to a reasonable restriction on communication complexity. We provide further support for the conjecture in the multipartite case. We show that any multipartite communication complexity problem could be reduced to triviality, had Nature been more non-local than quantum-mechanics by a quite small gap for any number of parties. Intriguingly, the multipartite nonlocal-box that we use to show the result corresponds to the generalized Bell inequality that manifests maximal violation in respect to a local hidden-variable theory.

quant-ph↗

arXiv2007

Scaling and universality of multipartite entanglement at criticality

Using the geometric entanglement measure, we study the scaling of multipartite entanglement in several 1D models at criticality, specifically the linear harmonic chain and the XY spin chain encompassing both the Ising and XX critical models. Our results provide convincing evidence that 1D models at criticality exhibit a universal logarithmic scaling behavior ~(c/12)log l in the multipartite entanglement per region for a partition of the system into regions of size l, where c is the central charge of the corresponding universality class in conformal field theory.

quant-ph↗

arXiv2007

Combined Electric and Magnetic Aharonov-Bohm Effects

It is well-known that the electric and magnetic Aharonov-Bohm effects may be formally described on equal footing using the four-vector potential in a relativistic framework. We propose an illustrative manifestation of both effects in a single configuration, in which the specific path of the charged particle determines the weight of the electric and magnetic acquired relative phases. The phases can be distinctively obtained in the Coulomb gauge. The scheme manifests the pedagogical lesson that though each of the relative phases is gauge-dependent their sum is gauge-invariant.

quant-ph↗

arXiv2004

BCS-like Modewise Entanglement of Fermion Gaussian States

We show that with respect to any bipartite division of modes, pure fermion gaussian states display the same type of structure in its entanglement of modes as that of the BCS wave function, namely, that of a tensor product of entangled two-mode squeezed fermion states. We show that this structure applies to a wider class of "isotropic" mixed fermion states, for which we derive necessary and sufficient conditions for mode entanglement.

quant-ph↗

arXiv2004

Violating Bell's inequalities in the vacuum

We employ an approach wherein vacuum entanglement is directly probed in a controlled manner. The approach consists of having a pair of initially nonentangled detectors locally interact with the field for a finite duration, such that the two detectors remain causally disconnected, and then analyzing the resulting detector mixed state. It is demonstrated that the correlations between arbitrarily far-apart regions of the vacuum of a relativistic free scalar field cannot be reproduced by a local hidden-variable model, and that as a function of the distance L between the regions, the entanglement decreases at a slower rate than exp(-(L/cT)^3).

quant-ph↗

arXiv2004

On the efficiency of nonlocal gates generation

We propose and study a method for using non-maximally entangled states to implement probabilistically non-local gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequences, the method becomes more efficient at a certain range of parameters. Gates of the form $\exp[iξσ_{n_A}σ_{n_B}]$ with $ξ\ll1$, can be implemented with nearly unit probability and with vanishingly small entanglement, while for the distillation-based method the gate is produced with a vanishing success probability. We also derive an upper bound to the optimal success probability and show that in the small entanglement limit, the bound is tight.

quant-ph↗

arXiv2004

Spatial structures and localization of vacuum entanglement in the linear harmonic chain

We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled gaussian states discussed in \cite {modewise}. We find that the resulting entangled mode shape hierarchy shows a distinctive layered structure with well defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We re-derive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class, and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite size regions is connected with the localization of the highest frequency innermost modes.

quant-ph↗

arXiv2004

Not So SuperDense Coding - Deterministic Dense Coding with Partially Entangled States

The utilization of a $d$-level partially entangled state, shared by two parties wishing to communicate classical information without errors over a noiseless quantum channel, is discussed. We analytically construct deterministic dense coding schemes for certain classes of non-maximally entangled states, and numerically obtain schemes in the general case. We study the dependency of the information capacity of such schemes on the partially entangled state shared by the two parties. Surprisingly, for $d>2$ it is possible to have deterministic dense coding with less than one ebit. In this case the number of alphabet letters that can be communicated by a single particle, is between $d$ and 2d. In general we show that the alphabet size grows in "steps" with the possible values $ d, d+1, ..., d^2-2 $. We also find that states with less entanglement can have greater communication capacity than other more entangled states.

quant-ph↗

arXiv2003

Quantum Error Correction in the Zeno Regime

In order to reduce errors, error correction codes (ECCs) need to be implemented fast. They can correct the errors corresponding to the first few orders in the Taylor expansion of the Hamiltonian of the interaction with the environment. If implemented fast enough, the zeroth order error predominates and the dominant effect is of error prevention by measurement (Zeno Effect) rather than correction. In this ``Zeno Regime'', codes with less redundancy are sufficient for protection. We describe such a simple scheme, which uses two ``noiseless'' qubits to protect a large number, $n$, of information qubits from noise from the environment. The ``noisless qubits'' can be realized by treating them as logical qubits to be encoded by one of the previously introduced encoding schemes.

quant-ph↗

arXiv2003

Deterministic linear optics quantum computation utilizing linked photon circuits

We suggest an efficient scheme for quantum computation with linear optical elements utilizing "linked" photon states. The linked states are designed according to the particular quantum circuit one wishes to process. Once a linked-state has been successfully prepared, the computation is pursued deterministically by a sequence of teleportation steps. The present scheme enables a significant reduction of the average number of elementary gates per logical gate to about 20-30 CZ_{9/16} gates.

quant-ph↗

arXiv2003

Entanglement from the vacuum

We explore the entanglement of the vacuum of a relativistic field by letting a pair of causally disconnected probes interact with the field. We find that, even when the probes are initially non-entangled, they can wind up to a final entangled state. This shows that entanglement persists between disconnected regions in the vacuum. However the probe entanglement, unlike correlations, vanishes once the regions become sufficiently separated. The relation between entropy, correlations and entanglement is discussed.

quant-ph↗