Quantum Bayesianism Says Reality Requires an Observer
The recent philosophy of Quantum Bayesianism, or QBism, rep- Einstein- Podolsky-Rosen (EPR) scenario involving entangled systems is also teed a priori In relation to the EPR challenge, I refer of course to the. A system's density matrix can be written in the form you cite if and only if it is a classical mixture of factorisable pure states. A factorisable pure state is, of course, . So particles can be in two places at once, or communicate . Hardy's rules governing possible states and their relationship to such as wavelike interference and entanglement, in which the properties of . A further approach in the spirit of quantum reconstruction is called quantum Bayesianism, or QBism.
A NOT gate is a device that takes a bit as input and produces as output either a 1 if the input is 0, or a 0 if the input is 1. In other words, a NOT gate is a 1-bit gate that flips the input bit. A controlled-NOT gate, or CNOT gate, takes two bits as inputs, a control bit and a target bit, and flips the target bit if and only if the control bit is 1, while reproducing the control bit. So there are two inputs, the control and target, and two outputs: A CNOT gate functions as a copying device for the control bit if the target bit is set to 0, because the output of the target bit is then a copy of the control bit: Insofar as we can think of a measurement as simply a copying operation, a CNOT gate is the paradigm of a classical measuring device.
Imagine Alice equipped with such a device, with input and output control and target wires, measuring the properties of an unknown classical world. The input control wire is a probe for the presence of absence of a property, represented by a 1 or a 0. The target wire functions as the pointer, which is initially set to 0.
- Quantum Entanglement and Information
- Quantum-Bayesian and Pragmatist Views of Quantum Theory
- Towards Better Understanding QBism
The output of the target is a 1 or a 0, depending on the presence or absence of the property. Suppose we attempt to use a CNOT gate to copy an unknown qubit state. Since we are now proposing to regard the CNOT gate as a device for processing quantum states, the evolution from input states to output states must be effected by a physical quantum transformation.
Quantum transformations are linear on the linear state space of qubits. Such superpositions — e. Linearity of the transformation requires that a transformation should take a qubit state represented by the sum of two orthogonal qubits to a new qubit state that is the sum of the transformed orthogonal qubits. If the CNOT gate succeeds in copying two orthogonal qubits, it cannot succeed in copying a linear superposition of these qubits.
Since the gate functions linearly, it must instead produce a state that is a linear superposition of the outputs obtained for the two orthogonal qubits. That is to say, the output of the gate will be represented by a quantum state that is a sum of two terms, where the first term represents the output of the control and target for the first qubit, and the second term represents the output of the control and target for the second orthogonal qubit. Quantum Cryptography Suppose Alice and Bob are separated and want to communicate a secret message, without revealing any information to Eve, an eavesdropper.
In fact, this is the only secure way to achieve perfect security in a classical world. To send a message to Bob, Alice communicates which bits in the key Bob should flip.
The resulting sequence of bits is the message. In addition, they would need to have some way of encoding messages as sequences of bits, by representing letters of the alphabet and spaces and punctuation symbols as binary numbers, which could be done by some standard, publicly available scheme. The problem is that messages communicated in this way are only secret if Alice and Bob use a different one-time pad for each message.
If they use the same one-time pad for several messages, Eve could gain some information about the correspondence between letters of the alphabet and subsequences of bits in the key by relating statistical features of the messages to the way words are composed of letters.
To share a new key they would have to rely on trusted couriers or some similar method to distribute the key. There is no way to guarantee the security of the key distribution procedure in a classical world.
Copying the key without revealing that it has been copied is also a problem for the shared key that Alice and Bob each store in some supposedly secure way.
But the laws of physics in a classical world cannot guarantee that a storage procedure is completely secure, and they cannot guarantee that breaching the security and copying the key will always be detected. So apart from the key distribution problem, there is a key storage problem. Moreover, any attempt by Eve to measure the quantum systems in the entangled state shared by Alice and Bob will destroy the entangled state.
Alice and Bob can detect this by checking a Bell inequality. One way to do this is by a protocol originally proposed by Artur Ekert. They communicate the directions of their polarization measurements publicly, but not the outcomes, and they divide the measurements into two sets: For the first set, when they measured the polarization in the same direction, the outcomes are random but perfectly correlated in the entangled state so they share these random bits as a cryptographic key.
They use the second set to check a Bell inequality, which reveals whether or not the entangled state has been destroyed by the measurements of an eavesdropper. While the difference between classical and quantum information can be exploited to achieve successful key distribution, there are other cryptographic protocols that are thwarted by quantum entanglement. Bit commitment is a key cryptographic protocol that can be used as a subroutine in a variety of important cryptographic tasks.
In a bit commitment protocol, Alice supplies an encoded bit to Bob. The information available in the encoding should be insufficient for Bob to ascertain the value of the bit, but sufficient, together with further information supplied by Alice at a subsequent stage when she is supposed to reveal the value of the bit, for Bob to be convinced that the protocol does not allow Alice to cheat by encoding the bit in a way that leaves her free to reveal either 0 or 1 at will.
To illustrate the idea, suppose Alice claims the ability to predict advances or declines in the stock market on a daily basis. To substantiate her claim without revealing valuable information perhaps to a potential employer, Bob she suggests the following demonstration: The safe will be handed to Bob, but Alice will keep the key.
At the end of the day's trading, she will announce the bit she chose and prove that she in fact made the commitment at the earlier time by handing Bob the key.
Of course, the key-and-safe protocol is not provably secure from cheating by Bob, because there is no principle of classical physics that that prevents Bob from opening the safe and closing it again without leaving any trace. The question is whether there exists a quantum analogue of this procedure that is unconditionally secure: Bob can cheat if he can obtain some information about Alice's commitment before she reveals it which would give him an advantage in repetitions of the protocol with Alice.
Most variants of the Copenhagen interpretation, however, hold that the outcomes of experiments are agent-independent pieces of reality for anyone to access.
Specifically, QBism posits that quantum theory is a normative tool which an agent may use to better navigate reality, rather than a mechanics of reality. Furthermore, not all authors who advocate views of this type propose an answer to the question of what the information represented in quantum states concerns.
In the words of the paper that introduced the Spekkens Toy Modelif a quantum state is a state of knowledge, and it is not knowledge of local and noncontextual hidden variables, then what is it knowledge about? We do not at present have a good answer to this question. We shall therefore remain completely agnostic about the nature of the reality to which the knowledge represented by quantum states pertains.
This is not to say that the question is not important. Rather, we see the epistemic approach as an unfinished project, and this question as the central obstacle to its completion.
Quantum Entanglement and Information (Stanford Encyclopedia of Philosophy)
Nonetheless, we argue that even in the absence of an answer to this question, a case can be made for the epistemic view. The key is that one can hope to identify phenomena that are characteristic of states of incomplete knowledge regardless of what this knowledge is about. In the Brukner—Zeilinger interpretation, a quantum state represents the information that a hypothetical observer in possession of all possible data would have.
Put another way, a quantum state belongs in their interpretation to an optimally-informed agent, whereas in QBism, any agent can formulate a state to encode her own expectations. Streater argued that "[t]he first quantum Bayesian was von Neumann ," basing that claim on von Neumann's textbook The Mathematical Foundations of Quantum Mechanics.
One important distinction between the two interpretations is their philosophy of probability: The goal of these research efforts has been to identify a new set of axioms or postulates from which the mathematical structure of quantum theory can be derived, in the hope that with such a reformulation, the features of nature which made quantum theory the way it is might be more easily identified. Once he makes a measurement, then he knows. Conceived by quantum theorist Christopher Fuchsthis observer-centric view of quantum mechanics is called Quantum Bayesianism, or QBism for short.
When the dealer puts a card face down, that card is simultaneously all 52 cards at once. In traditional quantum mechanicsthat's a concept known as superposition, and the mathematical formula that describes all of those states is called a wavefunction.
Only when you pick that card up and look at it does it "choose" its identity also known as "collapsing the wavefunction". Likewise, if all the cards are dealt so that you know that only the ace of spades and the queen of hearts remain, and you are dealt the ace of spades, that changes the state of the remaining card so it becomes the queen of hearts.
That relationship where the state of one card changes the state of the other is a concept called entanglement. Here's how QBism sees that same card game. When the dealer puts a card face down, a player knows that the card has a 1 in 52 chance of being any one of the cards in the deck; a 1 in 4 chance of being any one of the suits, and a 1 in 2 chance of being red or black.
According to QBism, that's all a wavefunction: When he turns the card over, instead of the card "choosing" to be, say, the ace of spades, the player just updates his knowledge: That card now has a percent chance of being the ace of spades.