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arXiv:quant-ph/0310185

Communication through measurements and unitary transformations

Bart D’Hooghe

Published Oct 30, 2003• 1 citation
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Abstract

It is generally accepted that no `faster than light signalling' (FTLS) using two entangled spin 1/2 particles is possible because of indeterminism in a quantum measurement and linearity of standard quantum mechanics. We show how in principle one bit of information could be transmitted using local measurements and a global unitary transformation of the state of two entangled spatially separated spin 1/2 particles. Assuming that the postulate of a state collapse due to measurement is valid, the no FTLS condition is saved if we do not have physical access to the required global unitary transformation. This means that the no FTLS condition is also present on the operational level, namely as imposing a physical restriction on the possible realizable unitary transformations, in this case of two entangled but spatially separated spin 1/2.

DOI
10.48550/arxiv.quant-ph/0310185

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It is generally accepted that no `faster than light signalling' (FTLS) using two entangled spin 1/2 particles is possible because of indeterminism in a quantum measurement and linearity of standard quantum mechanics. We show how in principle one bit of information could be transmitted using local measurements and a global unitary transformation of the state of two entangled spatially separated spin 1/2 particles. Assuming that the postulate of a state collapse due to measurement is valid, the no FTLS condition is saved if we do not have physical access to the required global unitary transformation. This means that the no FTLS condition is also present on the operational level, namely as imposing a physical restriction on the possible realizable unitary transformations, in this case of two entangled but spatially separated spin 1/2.
It is possible to use two particles (A and B) with entangled properties to transmit information at faster than light speeds. This can be done, not by trying to modulate the results of how particle A is measured, but by modulating whether particle A is measured or not measured. The effect of this modulating method is to place particle B in either a single value (but arbitrary) state or leave it in a superposition of states. It is then possible for the reciever of particle B to distinguish between these two states by the use of an appropriately designed interferometer. Such a device can be designed to produce an interference pattern only when particle B is in a superposition of values and a straight simple image when particle B has a single (arbitrary) defined value. Under the Copenhagen interpretation and existing experimental results, this method will produce a way of signalling fater than light. It will require the use of multiple entangled pairs of particles to effectively transmit a single bit of information. Under the Multi-Worlds Interpretation, it will not be so easy to communicate faster than light by this mechanism, as detector B will be detecting photon B as a superposition of values in both cases.
Present understanding of non-possibility of Quantum communication rests on analysis of possibility of signalling within a Quantum system. Is it possible to achieve signalling by a setup where the system is changed from one to another where the act of change serves as the signal and the change in the measurement probabilities would be detected and deciphered at the receiver end? A proposal is made where a variant of Delayed Choice Quantum Eraser experiment setup of Kim et al is used to achieve the same. The setup is also designed such that the speed of communication can be faster than light. NonLocality and Quantum communication Nonlocality is a feature of Quantum Mechanics that has been firmly established through experiments [Aspect et al, 1981] and well accepted now. Entangled particles separated by a distance still are part of one entity and when that entity changes state by a measurement in one part of it the change happens instantaneously across the domain the entity pervades. Is it possible to use this instantaneous state change to transmit information across at high speeds, faster than light (FTL)? This issue has been dealt with from the time the Einstein raised the EPR paradox [Einstein et al,1935] and has been claimed to be impossible and shown to be so by Peres, [Peres and Tenko, 2004] through the no-communication theorem which shows that any amount of signalling by Alice through measurements done at one end of the quantum system would not be sufficient for Bob to detect and decipher at the other end of the system. However the discussions in literature (as above) always deal with information transfer within a stable quantum system by making measurements at one end and analysing the possibility of detecting it at the other end. Peres and Tenko analyse a Quantum System S of mixed-state where Alice and Bob make measurements at their ends of the system. The authors derive the probability that Bob’s outcome is ν as
In this paper, without any priori assumption about the post-measurement state of system, we will examine how this state is restricted by assuming each of these following assumptions. First, by using this reasonable assumption that two successive measurements should be describable as one measurement. Second, by assuming the impossibility of faster than light signaling, "No-signaling condition". However, only by using these assumptions it is not possible to obtain the usual projection postulate. Instead, by means of a simple lemma, we will show that the density operator of system after a measurement is a linear function of the density operator determined by the usual post-measurement postulate. Furthermore we will show this linear function has a Kraus representation. Finally, we will discuss about the physical meaning of this consequence.
In this paper we present a theoretical analysis of the faster than light communication possibility based on entangled photons. We analyze designs that may be capable to solve the problem of direct information transfer between members of an entangled photon pairs. We consider that experimental verifications can confirm or even refute this. Our hypothesis was that most proofs of the nocommunication theorem are based on a certain set of conditions, and it is possible to provide a broader set of conditions that allow the establishment of entangled states as quantum information channels, without using a classical channel. One basic unit of the proposed design transforms the polarization state of one member of an entangled photon pair into a spatial superposition state. Thus, after the polarization measurement performed on one member, which eliminates the entanglement, the quantum information is maintained in the spatial superposition state of the other member. This can be recovered by a particular measurement based on spatial interference. We have shown that solutions with so-called symmetric functions lead to average results that corresponds to the nocommunication theorem. However, using asymmetric functions the averaged measurement results calculated in a prescribed time window can distinguish the types of measurements performed on the other member of the pair. This can establish a communication code that enables faster-than-light information sharing under specific conditions. There may be also further theoretical consequences: a significant extension of the quantum mechanical nonlocality principle.
It is shown that an ideal measurement of a one-particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light-crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one-particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh–DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom–qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light-crossing time of the cavity.
It is shown that an ideal measurement of a one–particle wave packet state of a relativistic quantum field in Minkowski spacetime enables superluminal signalling. The result holds for a measurement that takes place over an intervention region in spacetime whose extent in time in some frame is longer than the light crossing time of the packet in that frame. Moreover, these results are shown to apply not only to ideal measurements but also to unitary transformations that rotate two orthogonal one–particle states into each other. In light of these observations, possible restrictions on the allowed types of intervention are considered. A more physical approach to such questions is to construct explicit models of the interventions as interactions between the field and other quantum systems such as detectors. The prototypical Unruh-DeWitt detector couples to the field operator itself and so most likely respects relativistic causality. On the other hand, detector models which couple to a finite set of frequencies of field modes are shown to lead to superluminal signalling. Such detectors do, however, provide successful phenomenological models of atom-qubits interacting with quantum fields in a cavity but are valid only on time scales many orders of magnitude larger than the light crossing time of the cavity.