Quantum information and the information paradox

In science, unpredictability, whether product of observations or peculiar theoretical implications, is something that scientists have to consider. When an observation demonstrates a behavior contrary to what would be indicated by a consolidated theory, this occurrence is categorized as "anomaly". Consider, hypothetically, that you buy an avengers comicbook. By opening it you realize that the classic characters are drawn on each page of the notebook. However, as you continue to leaf through the pages, you observe Batman on a single page, which results in an immediate strangeness, as such an observation was not expected and is extremely unlikely. Batman's presence in the context would represent an anomaly. However, if Batman`s presence made sense in the story told, we could be reading a crossover story, thus dysmistifying the anomalous aspect of it. Furthermore, theoretical developments (or observations) may imply the appearance of scientific paradoxes, which indicate situations without solution. In theoretical physics there are some famous paradoxes, which, to this day, remain without definitive solution (they have only proposals). Two of the most famous examples are the information paradox and the EPR paradox.

To understand the problem presented by the paradox of information we must first understand the concept of quantum information. In our daily life (macroscopic world), we can observe various forms of information. Let's consider a car. The brand, color, model, power, speed, are all examples of information that can be taken from such an object. In computation and information theory, the smallest possible unit of information is the so-called bit, which can assume only two values, 0 or 1. Three bits can be organized into 8 distinct states, individually, given the possible combinations between 0 and 1. In quantum mechanics, the concept of information is close to that used in computing. In the same sense that bits are the smallest unit of information, so are the qubits (or quantum bits). However, qubits have an advantage because each qubit can be simultaneously in a state of superposition between the states |0⟩ and |1⟩. Thus, for every 1 qubit added in a sequence, the number of simultaneous states doubles, thus characterizing the advantage and power of quantum computers, which use this concept (see photo 2). In the language of quantum mechanics, qubits are represented by state vectors, representing two-level systems. But what do we mean by that? Let's consider the spin of an electron. Let's choose the z-axis for measuring the electronic spin. Before the measurement act, the state is in overlap; in this way, the direction of the spin can be either of the two possible orientations, pointing to +z ("up") or -z ("down"). Mathematically, such a state is represented by | φ_z ⟩=(1/√2)|0⟩+(1/√2)|1⟩, being (1/√2) the coefficients, whose square provides the probability that, given the measurement, the state is to be found in the |0 setting⟩ (representing the spin pointing to "down") or in the |1 setting⟩ (representing the spin pointing to "up"). The Bloch Sphere (photo 3) provides a way of visualizing the electronic spin. We can extend the list of quantum information examples to properties such as position and speed. The information can also be related to how objects differ. A set of carbon atoms, in a given arrangement, can result in graphite. A set with these same atoms, but in another arrangement, can result in a diamond. Quantum information makes the distinction possible.

When objects are captured by black holes, they will never escape, given the fact that the escape velocity beyond the event horizon is higher than that of light. Let's think of a diamond falling into a black hole. After crossing the event horizon, we no longer have access to what configuration this set of carbon atoms is. In this sense, quantum information is preserved, maintaining coherence with the principle of quantum information conservation, which says that quantum information can never be destroyed (this principle must be taken as fundamental and inviolable, and, in addition to the physical sense, it has rigorous mathematical foundations). However, if we consider the Hawking radiation described in the previous chapter, the black hole will slowly evaporate until it completely disappears. With that in mind, the situation changes, where did the information go? Was it destroyed? Erased? What happened to our diamond? These considerations are products of what has come to be called the "information paradox".

There is no definitive solution to the information paradox, but there are some proposals that try to solve it. Let's start with the most similar to science fiction. It may be possible that the information, when entering a black hole, ends up in another universe. In this case, although we still do not have access to information, it would be preserved. Alternatively, some scientists point out that the information of matter consumed by the black hole would be transcribed, somehow, into Hawking's radiation itself, while others indicate that the paradox is simply due to the lack of a theory of everything (unifying theory between relativity and quantum mechanics).

Although the paradox remains a mystery, Stephen Hawking, along with Malcolm Perry and Andrew Strominger, proposed an explanation of how black holes "store" the information they consume. The proposal says that information of all matter that falls into the black hole is "translated" to be "stored" on the event horizon of the black hole. Thus, the more matter the black hole consumes, the more mass it will acquire, which will increase its event horizon, thus enabling more information to be "stored". This idea, called supertranslation, can have extreme implications for our understanding of the cosmos. The interesting point is, if three-dimensional materials can be transformed/translated into a two-dimensional surface* (event horizon), could the same be applied to the entire universe? Is the universe, in its three-dimensionality, a projection, a hologram? This question became known as the "holographic principle" and, although we do not have the evidence (at least to this day), it provides new means of envisioning the universe and new possibilities of exploration of it.

* two-dimensional surface: the term, despite being redundant, was used to highlight the dimensionality considered. Photo 1: black hole and its gravitational lens Photo 2: bit and qubit Photo 3: Bloch Sphere Reference material: Black Holes; The Universe in a Nutshell; Brief Answers to Big Questions (Stephen Hawking) 50 Quantum Physics Ideas You Really Need to Know (Joanne Baker) https://youtu.be/r5Pcqkhmp_0 https://youtu.be/9XkHBmE-N34 https://youtu.be/HF-9Dy6iB_4 https://youtu.be/yWO-cvGETRQ