According to the IEP,
scientific realism is the view that well-confirmed scientific theories are approximately true; the entities they postulate do exist; and we have good reason to believe their main tenets
The Copenhagen interpretation is often summarized as “shut up and compute” with respect to the outcomes of measurements. Given that it does not give a pictorial representation/explanation of reality, would this technically be classified as an “antirealist” theory?
To characterize the Copenhagen interpretation as " 'Shut up and compute' with respect to the outcome of measurement" is no serious basis to deal with this interpretation of quantum mechanics.
Heisenberg, one of the proponents of the Copenhagen interpretation, devoted several chapters of his book “Physics and Philosophy” to this subject.
See Physics and Philosophy, chapters "III. The Copenhagen Interpretation of Quantum Theory" and chapter "VIII. Criticism and Counterproposals to the Copenhagen Interpretation of Quantum Theory".
IMO the main topic of the Copenhagen interpretation is to understand the relation between the world of possibilities and reality, i.e. the world of actual observation.
Please base your question on primary sources, not on some flippant comment from a dubious provenience.
And make precise which version of anti-realism you do consider: What do you take as the positive claims of anti-realism to use as basis and context of your question?
The Copenhagen interpretation is not a theory but a collection of views and interpretations that have a lot in common. It seems to me that it is indeed anti-realist.
Heisenberg wrote in Physics and Philosophy:
the idea of an objective real world, whose smallest parts exist independently of whether or not we observe them (..) is impossible.
Bohr wrote in Atomic Theory and the Description of Nature:
There is no quantum world. Isolated material particles are abstractions, their properties on the quantum theory being definable and observable only through their interaction with other syststems.
This led to firm opposition from Einstein who favoured a realist approach, quipping: I like to think that the moon is there, even when I'm not looking at it.
And in the famous Einstein-Podolsky-Rosen paper:
If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.
This is also known as the EPR criterion of reality. In order to save reality we must accept some form of hidden variables. John Bell showed in his 1964 theorem (together with Bob and Alice) that these hidden variables are not possible. This was later experimentally verified by Alain Aspect. Reality based on this criterion, when it comes to observables on the quantum level, then doesn't exist according to the Copenhagen interpretation.
I would say that you are questioning the value of a philosophical attribute that quantum theory is not intended to possess. Some physicists might have views on what QM means, but the formalism itself is independent of those views. The Copenhagen Interpretation implicitly assumes certain things are real, namely space, time, observables, potentials. The obvious anti-real element is the wave function, which is taken to be a mathematical quantity.
Given your quote from IEP, I would say that QM is a well established theory that is approximately true (in the sense that the results it produces are closely aligned with experimental results), we have good reason to believe its main tenets, and most of the entities it postulates- explicitly or implicitly, exist in the plain sense of that word. The key exception is the wave-function, the status of which remains disputed.
John Bell explored this question, basically in dialog with Einstein. Both were seeking to defend realism. Einstein was also seeking to defend locality.
In their work they defined realism and locality in these ways:
The answer by Philomath cites the definition of realism from the EPR paper. "Without disturbing the system" is the key phrase that if it cannot be satisfied, includes an observer in reality. Another key phrase is "we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity". There is consensus among physicists that based on the Heisenberg Uncertainty Principle, we can never specify any pair of physical quantities explicitly within the limits of HUP, so the Uncertainty Principle limits "realism" to only a close approximation of our universe. Additionally, under the Copenhagen theory of QM, there is not a defined value to physical quantities prior to a measurement. So Copenhagen can never be fully realist per HUP, and is not realist at all based on quantum uncertainty before measurement.
Einstein was not just defending realism and relativity, he was also trying to defend determinism. Einstein proposed a Hidden Variables Theory as an alternative QM theory to Copenhagen, which could satisfy both realism and locality, and allow our universe to be deterministic, but this model was tested and refuted.
Bell then showed how no alternative local hidden variable theories could ever match QM. He considered non-locality to be intrinsic to all QM theories. Bell's rationale has been experimentally supported by the discoveries of entanglement between particles that are outside a light-cone for interaction.
As an advocate for realism, and also for determinism, he defended the alternate quantum theory of Bohmian Mechanics. Bohmian Mechanics accepts non-locality, and extends it to not just a few esoteric cases of entangled particles, and instead assumes the entire universe is intrinsically entangled. Realism, rather than a stochastic universe, is necessary for determinism to be possible. Under BM, every quantum event is influenced by every other particle in the universe, no matter how far away, AND every particle has a defined location and other properties (contradicting the HUP).
Bohmian Mechanics is a competing quantum theory to QM, and is in principle testable against QM. Here is a blog summarizing the testing to date, which is trending against BM. https://settheory.net/Bohm In addition to the tests trending against BM, the intrinsic difficulty in performing calculations and making predictions under BM has made it a not very useable theory, and this has further limited its popularity among theoretical physicists. I also suspect that having to make assumptions about how much universe there is beyond our furthest observations, and its uniformity, may also detract from its attraction. A survey of theoretical physicists in 2016 found about 2% were advocates of Bohmian Mechanics.
There are other "interpretations" of QM, some of which are actually competing theories, and others of which may just be interpretations, as possible test cases between them and QM have not always been fleshed out. Einstein was particularly vigorous in clarifying that his "hidden variables interpretation" would make different predictions, and was therefore a competing theory. Other speculative theorizers have not been as vigorous, but over time, it has become clear that at least some of the other "interpretations" are actually competing theories, as with BM. Most of these testable differences are very difficult to test, and BM appears to have been the most evaluated different theory, other than HV.
Other than BM, the other interpretations of quanta are all stochastic, and accept HUP, and therefore are non-realist per Einstein and Bells' definition. They are also non-local.
