Quantum theory can be collectively verified

No theory of physics has been collectively scientifically verified in an experiment so far. It is pointed out that probabilistic structure of quantum theory can be collectively scientifically verified in an experiment. It is also argued that experimentalist’s point of view quantum theory is a complete theory. Generally, a proposed theory of physics is accepted by scientific community when it is experimentally verified. It can be expected that in principle a correct physical theory can be collectively as well as individually verified in an experiment. Otherwise the proposed physical theory cannot be called to be a scientific theory at all. It is well-known that Einstein was occupied with the idea of completeness of physical theory. Basically, the issue of completeness of physical theory initiated the great scientific debate [1,2] which is still continuing. Experimentalist’s point of view a physical theory may be considered to be a complete theory if the theory can be both individually as well as collectively verified in experiment. In the last century quantum theory, special and general theory of relativity have been repeatedly collectively verified without any ambiguity. But none of the collective verifications can be called scientific verification. The reason is, in the existing group work none of the members can scientifically rule out the possibility of manipulation of experimental data by other group members. Therefore, members of an experimental group cannot scientifically collectively claim these theories as correct theories. It is well-known that despite his own contribution to the initial development of quantum theory Einstein could not accept its probabilistic structure. “God does not play dice” is his famous comment on quantum theory. Can’t God(s) play dice for the verification of quantum theory ? Einstein never asked this question. The essence of quantum theory will be individually as well as collectively verified if its probabilistic structure -intrinsic randomness is individually as well as collectively verified. Collective verification of probabilistic structure of quantum theory means parties have to unanimously accept the outcome of quantum measurement. From the above discussion it can be understood that quantum theory can be collectively verified if uncontrollable/trustworthy random data can be collectively generated by quantum measurement. The issue of individual verification will be discussed later. It is still not known how to collectively generate uncontrollable/trustworthy random data even by classical means. This is considered to be a game-theoretic/cryptographic problem [3,4]. With the advent of quantum information the issue has been studied from that angle. It has been claimed [5] that uncontrollable random numbers/bits cannot be collectively generated within quantum theory even if noise is not considered. Interestingly, the proof allows collective generation of partly controllable non-random numbers within quantum theory. The claim was based on another claim [6,7]. As information processing is nothing but an experiment, so the claim [5] ultimately implies that quantum theory cannot be collectively verified in experiment. It means quantum theory cannot be called to be a scientific theory. It gives an extremely uneasy feeling, although many will take the conclusion as the most objectionable revelation in modern times. In the proofs [5-7] it is implicitly assumed [8-9] that bit value is encoded in a qubit – a two state quantum system. We have noticed [10] that existing quantum cryptosystems [8], based on qubit model of information processing, cannot provide security in communication without the support of classical cryptosystem. This conceptual problem can be overcome following alternative quantum coding (AQC) technique [10,11] wherein a sequence-ensemble of quantum states represents a bit. The proofs [5-7] have no binding on AQC. Following AQC uncontrollable random data can be generated in an information processing experiment. Suppose there is a stock of the following four EPR states of spin -1/2 particles. ( ) ↑ ↓ ± ↓ ↑ = ± 2 1 ψ ( ) ↓ ↓ ± ↑ ↑ = ± 2 1 φ Choosing the four EPR states at random the pairs XX can be arranged in two rows either in direct order or in reverse order. As for example, two pairs of arrangements of 20 EPR pairs are given below. 0 i S = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T} 0 j S = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T} i S = {A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T } j S = {T, S, R, Q, P, O, N, M, M, L, K, J, I, H, G, F, E, D, C, B, A} The same pair of letters denotes an EPR pair. The first pair of entangled sequences 0 i S and 0 j S , represent bit 0 and the second pair i S and 1 j S represent bit 1. It can be seen that density matrices associated with bit 0 and 1 are same; 1 0 ρ ρ = = 4 1 I . Suppose two parties, called Alice and Bob, know the basic quantum theory. Both Alice and Bob will jointly choose the EPR states to arrange them in two rows. We shall see that uncontrollable random data can be generated through bit commitment. So Alice will decide which pair of entangled sequences she will commit. Let us describe the experimental steps with some clarifications. 1. Alice collects N singlets A i X B i X where N need not to be large number (say, N = 50). If she collects singlets she verifies the rotational symmetry of the collected states choosing some states at random. 2. Alice applies unitary operators A i U ∈{ x σ , y σ , z σ , I} at random on each of her remaining particles A i X where x σ , y σ , z σ are Pauli matrices and I is 2× 2 identity matrix. The ensemble may be described [12] by ρ = 4 1 I where I is 4× 4 identity matrix. Alice transmits the particles B i X to Bob and stores the partners A i X in her quantum memory. 3. To verify the rotational symmetry of some of the shared states [12] Bob selects some particles B i X at random and requests Alice to send the partners A i X of his selected particles B i X converting the selected pairs A i X B i X into singlets. He keeps aside the remaining n particles (say n = 20) on quantum computer. 4. Alice applies the previously applied A i U ∈{ x σ , y σ , z σ , I} on partners A i X of Bob’s chosen particles B i X to convert the chosen pairs A i X B i X into singlets since I I σ σ σ 2 2 z 2 y 2 x = = = = . After this she sends the partners A i X of the chosen pairs A i X B i X to Bob. 5. Bob measures spin component of the pairs A i X B i X along a fixed axis or randomly chosen axes. If Bob gets 100% anti-correlated data he proceeds for the next step. 6. Bob applies unitary operators B i U ∈{ x σ , y σ , z σ , I} at random on the remaining n particles B i X . Thus Alice and Bob jointly choose the four EPR states at random to arrange them in two rows. 7. Alice measures the spin component of her remaining n particles A i X along z axis. 8. In this information processing experiment as an input Alice commits a bit 0 or 1 with probability 1/2. So Alice’s input is basically a string of random bits. To commit bit 0, Alice reveals results in direct order (Di). To commit bit 1, Alice reveals results in reverse order (Dn-i). Revealing results in direct or reverse order is tantamount to arranging EPR states in direct or reverse order. 9. As an input Bob guesses the bit and reveals his guess-bit to Alice. So Bob’s input is basically a string of random bits. 10. To reveal bit value Alice discloses the information of her A i U always in direct order. 11. Firstly, Bob measures the spin components of his particles along z axis. Secondly, from the available information of A i U and B i U Bob reconstructs the positions of the final EPR states in two rows. Bob matches their data with the reconstructed arrangements. If Bob gets 100% EPR data in direct order (DiDi ) the bit committed is 0. But if Bob gets 100% EPR data in reverse order (DiDn-i) the bit committed is 1. 12. If Bob’s guess is right, the protocol would generate a particular bit. If wrong it will generate the other bit. Suppose 11 = 1, 00 = 1 , 10 = 0 , 01 = 0. Note that 2 input combinations are possible. So 2 input combinations can output a particular predetermined bit. Thus in this information processing experiment two input strings of random bits generates an output string of random bits. Bob will pronounce the output string to Alice to confirm that he has indeed recovered the output string. 13. Alice and bob will verify/test the randomness of the output string. 14. After the verifications of shared entanglement and the randomness of the output string they are scientifically bound to accept that they have verified quantum theory due to the following proof. Let us prove that according to quantum theory the probability of jointly generating an uncontrollable bit by Alice and Bob is 1/2. In other words, bias given by Alice and Bob is zero;