# Quantum::Entanglement v.0.32

Quantum::Entanglement package contains QM entanglement of variables in perl. SYNOPSIS use Quantum::Entanglement qw(:DEFAULT :complex :QFT), my $c = entangle(1,0,i,1), # $c = |0> + i|1> my $d = entangle(1,0,1,1), # $d = |0> + |1> $e = $c * $d, # $e now |0*0> + i|0*1> + |1*0> + i|1*1>, connected to $c, $d if ($e == 1) { # observe, probabilistically chose an outcome # if we are here, ($c,$d) = i|(1,1)> print "* $e == 1n", } else { # one of the not 1 versions of $e chosen # if we are here, ($c,$d) = |(0,0)> + i|(1,0)> + |(0,1)> print "* $e != 1n", } BACKGROUND "Quantum Mechanics - the dreams that stuff is made of." Quantum mechanics is one of the stranger things to have emerged from science over the last hundred years. It has led the way to new understanding of a diverse range of fundamental physical phenomena and, should recent developments prove fruitful, could also lead to an entirely new mode of computation where previously intractable problems find themselves open to easy solution. While the detailed results of quantum theory are hard to prove, and even harder to understand, there are a handful of concepts from the theory which are more easily understood. Hopefully this module will shed some light on a few of these and their consequences. One of the more popular interpretations of quantum mechanics holds that instead of particles always being in a single, well defined, state they instead exist as an almost ghostly overlay of many different states (or values) at the same time. Of course, it is our experience that when we look at something, we only ever find it in one single state. This is explained by the many states of the particle collapsing to a single state and highlights the importance of observation. In quantum mechanics, the state of a system can be described by a set of numbers which have a probability amplitude associated with them. This probability amplitude is similar to the normal idea of probability except for two differences. It can be a complex number, which leads to interference between states, and the probability with which we might observe a system in a particular state is given by the modulus squared of this amplitude. Consider the simple system, often called a qubit, which can take the value of 0 or 1. If we prepare it in the following superposition of states (a fancy way of saying that we want it to have many possible values at once): particle = 1 * (being equal to 1) + (1-i) * (being equal to 0) we can then measure (observe) the value of the particle. If we do this, we find that it will be equal to 1 with a probability of 1**2 / (1**2 + (1-i)(1+i) ) and equal to zero with a probability of (1+i)(1-i) / (1**2 + (1-i)(1+i) ) the factors on the bottom of each equation being necessary so that the chance of the particle ending up in any state at all is equal to one. Observing a particle in this way is said to collapse the wave-function, or superposition of values, into a single value, which it will retain from then onwards. A simpler way of writing the equation above is to say that particle = 1 |1> + (1-i) |0> where the probability amplitude for a state is given as a multiplier of the value of the state, which appears inside the | > pattern (this is called a ket, as sometimes the bra or < |, pattern appears to the left of the probability amplitudes in these equations). Much of the power of quantum computation comes from collapsing states and modifying the probability with which a state might collapse to a particular value as this can be done to each possible state at the same time, allowing for fantastic degrees of parallelism. Things also get interesting when you have multiple particles together in the same system. It turns out that if two particles which exist in many states at once interact, then after doing so, they will be linked to one another so that when you measure the value of one you also affect the possible values that the other can take. This is called entanglement and is important in many quantum algorithms.

Quantum::Entanglement package contains QM ...

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