A system of two polarized photons in singlet state appears as being in one of two product states independent of any measurement. These states depend on the selected polarization angles. With the polarizers on either side perpendicular to each other, both photons pass the polarizers without any disturbance. Action at a distance is therefore not needed to explain the results of the measurements. In general, the elements of physical reality demanded by EPR are the polarization states of the two photons of the entangled pair. As these are local elements in the regions of space of the polarizers the EPR paradox for the case of entangled photons can be regarded as resolved.
A system of two polarized photons in singlet state appears as being in one of two product states independent of any measurement. These states depend on the selected polarization angles. With the polarizers on either side perpendicular to each other, both photons pass the polarizers without any disturbance. Action at a distance is therefore not needed to explain the results of the measurements. In general, the elements of physical reality demanded by EPR are the polarization states of the two photons of the entangled pair. As these are local elements in the regions of space of the polarizers the EPR paradox for the case of entangled photons can be regarded as resolved.
Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with an arbitrary axis of quantization. This axis acts as a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state. Whether or not the EPR spin pairs retain entanglement or disentangle, however, the statistical ensemble interpretation resolves the EPR paradox and gives a mechanism for quantum "teleportation" without the need for instantaneous action-at-a-distance.
Usual arguments on EPR state assume that, after particles I and II interact somewhere, they are spatially separated, which is why EPR correlation was considered to be a paradox. That is, after the interaction, particle I exists only in a spatial region A, while particle II exists only in a spatial region B located at a distance from A. However, though the separation imposes certain restriction on possible quantum state, its implication has not been properly considered. That is, though quantum state of A is a tensor product of quantum state of particle I and II in A, as quantum state of particle II in A is ground state only, the product is identical to quantum state of particle I in A. Similarly, quantum state of B is quantum state of particle II in B. Then, as entire quantum state is Cartesian, not tensor, product of quantum state of A and B, the entire quantum state is Cartesian product of quantum state of particle I and II, which means there is no tensor product term to represent quantum entanglement. For example, using binary state, (|0>, |0>) + (|1>, |1>) = (|0>, |1>) + (|1>, |0>) = (|0> + |1>, |0> + |1>). Separation process resolves entanglement. If the entire quantum state is calculated differently, by first taking Cartesian product and, then, tensor product, a tensor product term appears. However, as the term represents action at a distance and, thus, unphysical, its coefficient must always be 0. That is, quantum entanglement of EPR correlation assuming the spatial separation is a superficial mathematical artifact representing action at a distance.
If the excitation of a system of quantized fields with a given set of quantum numbers does not exist, the amplitude of the triggering of the source is zero. A system with a source of two photons in a singlet state and two photon detectors is considered in detail. It is shown that the condition of operation of one detector with a given direction of photon polarization uniquely determines the adequate choice of direction and polarization for the second detector. This conclusion is in accordance with the laws of motion and conservation of quantum numbers of excitations in a system of quantized fields.
One of the most intriguing concepts of quantum mechanics is quantum entanglement. Two physical systems are said to be entangled with respect to a certain variable, if their individual outcomes of the variable are undetermined before measurement, but strictly correlated. Measurement of the variable for only one system immediately determines the outcome for the other system, irrespective of the distance between the two systems. It is this strong correlation that provides a basis for perspective, powerful applications like quantum cryptography and quantum computation. The most studied entangled systems, often called EPR systems (after the pioneers Einstein, Podolsky and Rosen), are pairs of light particles or photon pairs. These photon pairs, usually generated via the optical process of a spontaneous parametric down-conversion, are, in principal, simultaneously entangled in three variables, being polarization (polarization entanglement), energy or time (time entanglement), and momentum or transverse space (spatial entanglement). The contents of this thesis cover new insights in the polarization and spatial entanglement of photons. We have investigated both the entanglement quality and the yield of entangled photons for different experimental geometries that are associated with the production and detection of the photons.
The famous EPR paradox shows that if we describe quantum particles in the usual way -- by their wave functions -- then we get the following seeming contradiction. If we entangle the states of the two particles, then move them far away from each other, and measure the state of the first particle, then the state of the second particle immediately changes -- which contradicts to special relativity, according to which such immediate-action-at-a-distance is not possible. It is known that, from the physical viewpoint, this is not a real paradox: if we measure any property of the second particle, the results will not change whether we perform the measurement on the first particle or not. What the above argument shows is that the usual wave function description of a quantum state does not always adequately describe the corresponding physics. In this paper, we propose a new, more physically adequate description of a quantum state, a description in which there is no EPR paradox: measurements performed at the first particle does not change the state of the remote second one.