Asher Peres

Separability Criterion for Density Matrices

A quantum system consisting of two subsystems is {ital separable} if its density matrix can be written as {rho}={summation}{sub {ital Aw}}{sub {ital A}}{rho}{prime}{sub {ital A}}{circle_times}{rho}{double_prime}{sub {ital A}}, where {rho}{prime}{sub {ital A}} and {rho}{double_prime}{sub {ital A}} are density matrices for the two subsystems, and the positive weights {ital w}{sub {ital A}} satisfy {summation}{ital w}{sub {ital A}}=1. In this Letter, it is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of {rho}, has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell{close_quote}s inequality for detecting quantum inseparability. {copyright} {ital 1996 The American Physical Society.}

Quantum cryptography with 3-state systems.

We consider quantum cryptographic schemes where the carriers of information are 3-state particles. One protocol uses four mutually unbiased bases and appears to provide better security than obtainable with 2-state carriers. Another possible method allows quantum states to belong to more than one basis. Security is not better, but many curious features arise.

How to differentiate between non-orthogonal states

Abstract An infinite sequence of generalized measurements, recently proposed by Ivanovic, can be performed in a single step. It is shown that the final result is the optimal one.

Two simple proofs of the Kochen-Specker theorem

A new proof of the Kochen-Specker theorem uses 33 rays, instead of 117 in the original proof. If the number of dimensions is increased from 3 to 4, only 24 rays are needed.

Unperformed experiments have no results

This paper discusses correlations between the results of measurements performed on physical systems which are widely separated, but have interacted in the past. It is shown that quantum correlations are stronger than classical correlations. This property leads to the following paradox, known as Bell’s theorem: Let us assume that the outcome of an experiment performed on one of the systems is independent of the choice of the experiment performed on the other. Now, let us try to imagine the results of alternative measurements, which could have been performed on the same systems instead of the actual measurements. Then there is no way of contriving these hypothetical results so that they will satisfy all the quantum correlations with the results of the actual measurements. However, the weaker classical correlations can be satisfied.

Incompatible results of quantum measurements

Abstract Quantum theory is incompatible with the following propositions. (1) The result of the measurement of an operator A depends solely on A and on the system being measured. (2) If operators A and B commute, the result of a measurement of their product AB is the product of the results of separate measurements of A and of B .

QUANTUM-STATE DISTURBANCE VERSUS INFORMATION GAIN : UNCERTAINTY RELATIONS FOR QUANTUM INFORMATION

When an observer wants to identify a quantum state, which is known to be one of a given set of nonorthogonal states, the act of observation causes a disturbance to that state. We investigate the trade-off between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable nonorthogonal pure states. \textcopyright{} 1996 The American Physical Society.

Gravitational radiation damping of nongravitational motion

Abstract A material system acted upon by internal forces much larger than the gravitational ones is considered, and the rate of work of this system against its own gravitational field is computed. The result is equal to the rate of radiated energy obtained from the linearized theory.

Quantum entropy and special relativity

We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

Zeno Paradox in Quantum Theory

The coupling of an unstable quantum system with a measuring apparatus alters the dynamical properties of the former, in particular, its decay law. The decay is usually slowed down and can even be completely halted by a very tight monitoring.