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Shahar Dolev

Publications and source records attributed to Shahar Dolev.

11 recordsLinked to original sources
arXiv2006

A quantum secret ballot

The paper concerns the protection of the secrecy of ballots, so that the identity of the voters cannot be matched with their vote. To achieve this we use an entangled quantum state to represent the ballots. Each ballot includes the identity of the voter, explicitly marked on the "envelope" containing it. Measuring the content of the envelope yields a random number which reveals no information about the vote. However, the outcome of the elections can be unambiguously decided after adding the random numbers from all envelopes. We consider a few versions of the protocol and their complexity of implementation.

quant-ph↗
arXiv2006

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.

quant-ph↗
arXiv2002

Is There More to T?

We present some novel results indicating that time's description in present-day physics is deficient. We use Hawking's information-erasure hypothesis to counter his own claim that time's arrow depends only on initial conditions. Next, we propose quantum mechanical experiments that yield inconsistent histories, suggesting that not only events but also entire histories might be governed by a more fundamental dynamics.

quant-ph↗
arXiv2002

Time-Reversed EPR and the Choice of Histories in Quantum Mechanics

When a single photon is split by a beam splitter, its two `halves' can entangle two distant atoms into an EPR pair. We discuss a time-reversed analogue of this experiment where two distant sources cooperate so as to emit a single photon. The two `half photons,' having interacted with two atoms, can entangle these atoms into an EPR pair once they are detected as a single photon. Entanglement occurs by creating indistinguishabilility between the two mutually exclusive histories of the photon. This indistinguishabilility can be created either at the end of the two histories (by `erasing' the single photon's path) or at their beginning (by `erasing' the two atoms' positions).

quant-ph↗
arXiv2001

Non-Sequential Behavior of the Wave Function

An experiment is presented in which the alleged progression of a photon's wave function is ``measured'' by a row of superposed atoms. The photon's wave function affects only one out of the atoms, regardless of its position within the row, thereby manifesting not only non-local but also non-sequential characteristics. It also turns out that, out of n atoms, each one has a probability which is higher than the normal 1/n to be the single affected one.

quant-ph↗
arXiv2001

Does Indeterminism Give Rise to an Intrinsic Time Arrow?

In any physical theory that admits true indeterminism, the thermodynamic arrow of time can arise regardless of the system's initial conditions. Hence on such theories time's arrow emerges out of the basic physical interactions. The example of the GRW theory is studied in detail.

quant-ph↗
arXiv2000

Black-Hole Uncertainty Entails an Intrinsic Time Arrow. a Note on the Hawking-Penrose Controversy

Any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. Only determinism enables time reversal of entropy increase. A contradiction therefore arises between two statements of Hawking. A simulation of a system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even slight failure of determinism occurs.

gr-qc↗
arXiv2000

Nonlocal Effects of Partial Measurements and Quantum Erasure

Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the EPR setting, we prove that i) every partial measurement nonlocally creates the same partial change in the distant particle; and ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps "traveling" back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial "which path" measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques where it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.

quant-ph↗
arXiv2000

Biology and Thermodynamics: Seemingly-Opposite Phenomena in Search of a Unified Paradigm

It is probably not a coincidence that two of the pioneers of thermodynamics, Helmholtz and Mayer, were physicians. Thermodynamics studies the transformations of energy, and such transformations ceaselessly take place in all living systems (probably with important differences between the states of health and disease). Moreover, thermodynamics studies the elusive notions of order and disorder, which are also, respectively, the very hallmarks of life and death. These similarities suggest that thermodynamics might provide a unifying paradigm for many life sciences, explaining the multitude of life's manifestations on the basis of a few basic physical principles. In this article we introduce some basic thermodynamic concepts and point out their usefulness for the biologist and the physician. We hope to show that thermodynamics enables looking at the riddles of life from a new perspective and asking some new fruitful questions.

physics.bio-ph↗
arXiv2000

Black Hole Evaporation Entails an Objective Passage of Time

Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We prove that any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. It is only determinism that enables time reversal, whether theoretical or experimental, of anyentropy-increasing process. A contradiction therefore arises between Hawking's argument that physical law is time-symmetric and his controversial claim that black-hole evaporation introduces a fundamental unpredictability into the physical world. The latter claim forcibly entails an intrinsic time-arrow independent of boundary conditions. A simulation of a simple system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even the slightest failure of determinism occurs. This proof is then extended to the classical behavior of black holes. We conclude with pointing out the affinity between time's arrow and its apparent passage.

quant-ph↗